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'''Risk''' is the potential of gaining or losing something of value.<ref>{{Cite web| url=http://iosrjournals.org/iosr-jbm/papers/Vol16-issue3/Version-3/K016338389.pdf| title=Risk Management - An Analytical Study| date=Feb 2014| accessdate=6 June 2016| work=IOSR Journal of Business and Management| pages=83–89}}</ref> Values (such as [[Wikipedia:physical health|physical health]], [[Wikipedia:social status|social status]], emotional well-being, or financial wealth) can be gained or lost when taking risk resulting from a given action or inaction, foreseen or unforeseen. Risk can also be defined as the intentional interaction with [[Wikipedia:uncertainity|uncertainty]].<ref>{{cite journal|last1=Cline|first1=Preston B. |title=The Merging of Risk Analysis and Adventure Education|journal=Wilderness Risk Management|date=3 March 2015|volume=5|issue=1|pages=43–45|url=http://www.nols.edu/nolspro/pdf/wrmc_proceedings_05_adventure_cline.pdf|accessdate=12 December 2016}}</ref> Uncertainty is a potential, unpredictable, and uncontrollable outcome.

Risk determined by 
* the uncertainty of an event and 
* the impact of an event
:<math> Risk = Probability \times Impact \qquad (\ast)</math> 
Risk analysis tried to derive estimators for the probability and expect impact of events. Risk management tries to define consequences of action taken in spite of uncertainty.<ref>{{cite journal|last1=Antunes|first1=Ricardo|last2=Gonzalez|first2=Vicente|title=A Production Model for Construction: A Theoretical Framework|journal=Buildings|date=3 March 2015|volume=5|issue=1|pages=209–228|doi=10.3390/buildings5010209|url=http://www.mdpi.com/2075-5309/5/1/209/htm|accessdate=17 March 2015}}</ref>

[[Risk Literacy]] is the ability to [[Wikipedia:Risk perception|perceive risk]] and take appropriate actions for risk mitigation

[[Wikipedia:Risk perception|Risk perception]] is the subjective judgment people make about the severity and probability of a risk, and may vary person to person. Furthermore the individual judgement might be contradiction to scientific data, that provides estimates for the probability and the propective impact of an event. 

The multiplicative structure of risk (see <math>(\ast)</math>) shows that even a very unlikely event like an accident can have a high risk, if the impact or loss is very high (e.g. Tschernobyl, Fukushima atomic power station accident). Any human endeavor carries some risk and a high risk is be determined by the probability and impact<ref>{{cite web|title=Risk|url=http://plato.stanford.edu/archives/spr2014/entries/risk/|work=The Stanford Encyclopedia of Philosophy|accessdate=9 May 2014|last1=Hansson |first1=Sven Ove|first2=Edward N. |last2=Zalta|date=Spring 2014}}</ref>. Considering the risk solely from the probability perspective is caused by the application of the term in our language
     "I have a high risk of getting ...."
does literally mean:
     "There is a high probabilty that I will get ...."  

== Definitions ==
[[File:3 Alarm Building Fire.jpg|thumb|Firefighters at work]]

The [[Wikipedia:Oxford English Dictionary|Oxford English Dictionary]] cites the earliest use of the word in English (in the spelling of ''risque'' from its from French original,  'risque' ) as of 1621, and the spelling as ''risk'' from 1655. It defines ''risk'' as:

<blockquote>(Exposure to) the possibility of loss, injury, or other adverse or unwelcome circumstance; a chance or situation involving such a possibility.<ref>[[Oxford English Dictionary]]</ref></blockquote>

# Risk is an uncertain event or condition that, if it occurs, has an effect on at least one [[Wikipedia:project|project]] objective. (This definition, using project terminology, is easily made universal by removing references to projects).<ref>A Guide to the Project Management Body of Knowledge (4th Edition) ANSI/PMI 99-001-2008</ref>
# The probability of something happening multiplied by the resulting cost or benefit if it does. (This concept is more properly known as the 'Expectation Value' or 'Risk Factor' and is used to compare levels of risk)
# The probability or threat of quantifiable damage, injury, liability, loss, or any other negative occurrence that is caused by external or internal vulnerabilities, and that may be avoided through preemptive action.
# [[Wikipedia:Finance|Finance]]: The possibility that an actual return on an investment will be lower than the expected return.
# [[Wikipedia:Insurance|Insurance]]: A situation where the probability of a variable (such as burning down of a building) is known but when a mode of occurrence or the actual value of the occurrence (whether the fire will occur at a particular property) is not.<sup>''(Reference needed)''</sup>  A risk is not an uncertainty (where neither the probability nor the mode of occurrence is known), a peril (cause of loss), or a hazard (something that makes the occurrence of a peril more likely or more severe).
# Securities trading: The probability of a loss or drop in value. Trading risk is divided into two general categories: (1) [[Wikipedia:Systemic risk|Systematic risk]] affects all securities in the same class and is linked to the overall capital-market system and therefore cannot be eliminated by diversification. Also called [[Wikipedia:market risk|market risk]]. (2) Non-systematic risk is any risk that isn't market-related. Also called non-market risk, extra-market risk or diversifiable risk.<!-- Needs sorting out -->
# [[Wikipedia:Workplace|Workplace]]: Product of the consequence and probability of a hazardous event or phenomenon. For example, the risk of developing cancer is estimated as the incremental probability of developing cancer over a lifetime as a result of exposure to potential carcinogens (cancer-causing substances).

=== International Organization for Standardization ===

The [[Wikipedia:International Organization for Standardization|International Organization for Standardization]] publication [[Wikipedia:ISO 31000|ISO 31000]] (2009) / ISO Guide 73:2002 definition of risk is the 'effect of uncertainty on objectives'. In this definition, uncertainties include events (which may or may not happen) and uncertainties caused by ambiguity or a lack of information. It also includes both negative and positive impacts on objectives. Many definitions of risk exist in common usage, however this definition was developed by an international committee representing over 30 countries and is based on the input of several thousand subject matter experts.

=== Other ===

Very different approaches to risk management are taken in different fields, e.g. "Risk is the unwanted subset of a set of uncertain outcomes" (Cornelius Keating).

:Risk can be seen as relating to the [[probability]] of uncertain future events.<ref name=FAIRW/>  For example, according to [[Wikipedia:Factor Analysis of Information|Factor Analysis of Information Risk|factor analysis of information risk]]], risk is:<ref name=FAIRW>[http://www.riskmanagementinsight.com/media/docs/FAIR_introduction.pdf "An Introduction to Factor Analysis of Information Risk (FAIR)", Risk Management Insight LLC, November 2006];.</ref> the probable frequency and probable magnitude of future loss.  In computer science this definition is used by [[Wikipedia:The Open Group|The Open Group]].<ref name=OGC081>Technical Standard Risk Taxonomy {{ISBN|1-931624-77-1}} Document Number: C081 Published by The Open Group, January 2009.</ref>

:OHSAS (Occupational Health & Safety Advisory Services) defines risk as the combination of the probability of a hazard resulting in an adverse event, and the severity of the event.<ref>"Risk is a combination of the likelihood of an occurrence of a hazardous event or exposure(s) and the severity of injury or ill health that can be caused by the event or exposure(s)" (OHSAS 18001:2007).</ref>

:In [[Wikipedia:information security|information security]] risk is defined as "the potential that a given [[Wikipedia:threat (computer)|threat]] will exploit [[Wikipedia:vulnerability (computing)|vulnerabilities]] of an [[Wikipedia:asset|asset]] or group of assets and thereby cause harm to the organization".<ref>ISO/IEC 27005:2008.</ref>

:[[Wikipedia:Financial risk|Financial risk]] is often defined as the unpredictable variability or [[Wikipedia:Volatility (finance)|volatility]] of returns, and this would include both potential better-than-expected and worse-than-expected returns. References to negative risk below should be read as also applying to positive impacts or opportunity (e.g. for "loss" read "loss or gain") unless the context precludes this interpretation.

:The related terms "[[Wikipedia:threat|threat]]" and "[[Wikipedia:hazard|hazard]]" are often used to mean something that could cause harm.

==Practice areas==
Risk is ubiquitous in all areas of life and risk management is something that we all must do, whether we are managing a major organization or simply crossing the road.  When describing risk however, it is convenient to consider that risk practitioners operate in some specific practice areas.

===Economic risk===

Economic risks can be manifested in lower incomes or higher expenditures than expected. The causes can be many, for instance, the hike in the price for raw materials, the lapsing of deadlines for construction of a new operating facility, disruptions in a production process, emergence of a serious competitor on the market, the loss of key personnel, the change of a political regime, or natural disasters.

===Health===
Risks in personal health may be reduced by [[Wikipedia:primary prevention|primary prevention]] actions that decrease early causes of illness or by [[Wikipedia:secondary prevention|secondary prevention]] actions after a person has clearly measured clinical signs or symptoms recognized as risk factors. Tertiary [[Wikipedia:prevention (medical)|prevention]] reduces the negative impact of an already established disease by restoring function and reducing disease-related complications. Ethical medical practice requires careful discussion of [[Wikipedia:risk factors|risk factors]] with individual patients to obtain [[Wikipedia:indormed consent|informed consent]] for secondary and tertiary prevention efforts, whereas public health efforts in primary prevention require education of the entire population at risk. In each case, careful communication about risk factors, likely outcomes and [[Wikipedia:certainty|certainty]] must distinguish between causal events that must be decreased and associated events that may be merely consequences rather than causes.

In epidemiology, the '''lifetime risk''' of an effect is the ''[[Wikipedia:cumulative incidence|cumulative incidence]]]'', also called ''incidence proportion'' over an entire lifetime.<ref>{{cite journal |journal=J Epidemiol Community Health |vauthors=Rychetnik L, Hawe P, Waters E, Barratt A, Frommer M |date=July 2004 |volume=58 |pages=538–45 |doi=10.1136/jech.2003.011585 |pmid=15194712 |pmc=1732833 |title=A glossary for evidence based public health |issue=7 }}</ref>

===Health, safety, and environment===
In terms of occupational health & safety management, the term 'risk' may be defined as the most likely consequence of a hazard, combined with the likelihood or probability of it occurring.

Health, safety, and environment (HSE) are separate practice areas; however, they are often linked. The reason for this is typically to do with organizational management structures; however, there are strong links among these disciplines. One of the strongest links between these is that a single risk event may have impacts in all three areas, albeit over differing timescales. For example, the uncontrolled release of radiation or a toxic chemical may have immediate short-term safety consequences, more protracted health impacts, and much longer-term environmental impacts. Events such as Chernobyl, for example, caused immediate deaths, and in the longer term, deaths from cancers, and left a lasting environmental impact leading to birth defects, impacts on wildlife, etc.

Over time, a form of risk analysis called environmental risk analysis has developed. Environmental risk analysis is a field of study that attempts to understand events and activities that bring risk to human health or the environment.<ref name="Environmental Risk Analysis: Problems and Perspectives in Different Countries">{{cite journal|last=Gurjar|first=Bhola Ram|author2=Mohan, Manju |title=Environmental Risk Analysis: Problems and Perspectives in Different Countries|journal=Risk: Health, Safety & Environment|year=2002|volume=13|page=3|url=http://heinonline.org/HOL/Page?handle=hein.journals/risk13&id=5&collection=journals&index=journals/risk|accessdate=23 March 2013}}</ref>

Human health and environmental risk is the likelihood of an adverse outcome (See [[Wikipedia:adverse outcome pathway|adverse outcome pathway]]). As such, risk is a function of hazard and exposure. Hazard is the intrinsic danger or harm that is posed, e.g. the toxicity of a chemical compound. Exposure is the likely contact with that hazard. Therefore, the risk of even a very hazardous substance approaches zero as the exposure nears zero, given a person's (or other organism's) biological makeup, activities and location (See [[Wikipedia:exposome|exposome]]).<ref>Vallero, Daniel A. (2016). "Environmental Biotechnology: A Biosystems Approach." Amsterdam: Academic Press. {{ISBN|978-0-12-407776-8}}.</ref> Another example of health risks are when certain behaviors, such as [[Wikipedia:risky sexual behavior|risky sexual behaviors]], increase the likelihood of contracting [[Wikipedia:HIV|HIV]].<ref name = Potter2013 >{{cite book | last = Potter | first = Patricia | title = Fundamentals of nursing | publisher = Mosby Elsevier | location = St. Louis, Mo | year = 2013 | isbn = 9780323079334 | page=386 }}</ref>

=== Social Aspects of Risk ===
Individual risk perception and risk taking can also be influenced by social factors. A study using representative household data in the US, Italy and Austria finds evidence that risk taking levels can be influenced by the immediate social environment and by the welfare regime of a state (i.e. different support networks). The study also finds that these factors can interact.<ref>{{Cite journal|last=Schneider|first=Claudia R.|last2=Fehrenbacher|first2=Dennis D.|last3=Weber|first3=Elke U.|title=Catch me if I fall: Cross-national differences in willingness to take financial risks as a function of social and state ‘cushioning’|url=http://www.sciencedirect.com/science/article/pii/S0969593117302160|journal=International Business Review|doi=10.1016/j.ibusrev.2017.03.008}}</ref>

===Information technology and information security===
'''Information technology risk''', or '''IT risk''', '''IT-related risk''', is a risk related to [[Wikipedia:information technology|information technology]]. This relatively new term was developed as a result of an increasing awareness that information security is simply one facet of a multitude of risks that are relevant to IT and the real world processes it supports.

The increasing dependencies of modern society on information and computers networks (both in private and public sectors, including military)<ref>
{{cite book |last1= Cortada|first1= James W.|authorlink1= |last2= |first2= |authorlink2= |editor1-first= |editor1-last= |editor1-link= |others= |title= The Digital Hand: How Computers Changed the Work of American Manufacturing, Transportation, and Retail Industries |trans_title= |url= |archiveurl= |archivedate= |format= |accessdate= |type= |edition= |series= |volume= |date=2003-12-04 |origyear= |publisher= Oxford University Press|location=USA|isbn= 0-19-516588-8 |oclc= |doi= |id= |pages= 512|at= |trans_chapter= |chapter= |chapterurl= |quote= |ref= |bibcode= |laysummary= |laydate= |separator= |postscript= |lastauthoramp=}}</ref><ref>{{cite book |last1= Cortada|first1= James W.|authorlink1= |last2= |first2= |authorlink2= |editor1-first= |editor1-last= |editor1-link= |others= |title= The Digital Hand: Volume II: How Computers Changed the Work of American Financial, Telecommunications, Media, and Entertainment Industries |trans_title= |url= |archiveurl= |archivedate= |format= |accessdate= |type= |edition= |series= |volume= |date=2005-11-03 |origyear= |publisher= Oxford University Press|location=USA|isbn= 978-0-19-516587-6 |oclc= |doi= |id= |page= |pages= |at= |trans_chapter= |chapter= |chapterurl= |quote= |ref= |bibcode= |laysummary= |laydate= |separator= |postscript= |lastauthoramp=}}</ref><ref>{{cite book |last1= Cortada|first1= James W.|authorlink1= |last2= |first2= |authorlink2= |editor1-first= |editor1-last= |editor1-link= |others= |title= The Digital Hand, Vol 3: How Computers Changed the Work of American Public Sector Industries  |trans_title= |url= |archiveurl= |archivedate= |format= |accessdate= |type= |edition= |series= |volume= |date=2007-11-06 |origyear= |publisher= Oxford University Press|location=USA|isbn= 978-0-19-516586-9 |oclc= |doi= |id= |pages= 496|at= |trans_chapter= |chapter= |chapterurl= |quote= |ref= |bibcode= |laysummary= |laydate= |separator= |postscript= |lastauthoramp=}}</ref> has led to new terms like [[Wikipedia:IT risk|IT risk]] and [[Wikipedia:Cyberwarfare|Cyberwarfare]].

'''Information security''' means protecting information and [[Wikipedia:information system|information systems]] from unauthorized access, use, disclosure, disruption, modification, perusal, inspection, recording or destruction.<ref>{{usc|44|3542}}(b)(1).</ref> Information security grew out of practices and procedures of [[Wikipedia:computer security|computer security]].<br />
Information security has grown to '''information assurance (IA)''' i.e. is the practice of managing risks related to the use, processing, storage, and transmission of information or data and the systems and processes used for those purposes. <br />
While focused dominantly on information in digital form, the full range of IA encompasses not only digital but also analog or physical form. <br />
Information assurance is interdisciplinary and draws from multiple fields, including [[accounting]], [[Wikipedia:fraud|fraud]] examination, [[Wikipedia:forensic science|forensic science]], [[Wikipedia:management science|management science]], [[Wikipedia:systems engineering|systems engineering]], [[Wikipedia:security engineering|security engineering]], and [[Wikipedia:criminology|criminology]], in addition to computer science.

So, ''[[#Information technology risk|IT risk]]'' is narrowly focused on computer security, while ''information security'' extends to risks related to other forms of information (paper, microfilm). ''Information assurance'' risks include the ones related to the consistency of the business information stored in IT systems and the information stored by other means and the relevant business consequences.

===Insurance===
[[Wikipedia:Insurance|Insurance]] is a risk treatment option which involves risk sharing. It can be considered as a form of contingent capital and is akin to purchasing an [[Wikipedia:Option (finance)|option]] in which the buyer pays a small premium to be protected from a potential large loss.

Insurance risk is often taken by insurance companies, who then bear a pool of risks including market risk, credit risk, operational risk, interest rate risk, mortality risk, longevity risks, etc.<ref>James M. Carson; Elyas Elyasiani; Iqbal Mansur(December 2008), "Market Risk, Interest Rate Risk, and Interdependencies in Insurer Stock Returns: A System-GARCH Model", ''The Journal of Risk and Insurance'', {{ISSN|0022-4367}}, 12/2008, Volume 75, Issue 4, pp. 873–891, doi: 10.1111/j.1539-6975.2008.00289.x</ref>

===Business and management===
Means of assessing risk vary widely between professions. Indeed, they may define these professions; for example, a doctor manages medical risk, while a civil engineer manages risk of structural failure. A [[Wikipedia:professional|professional]] [[Wikipedia:code of ethics|code of ethics]] is usually focused on risk assessment and mitigation (by the professional on behalf of client, public, society or life in general).

In the workplace, incidental and [[Wikipedia:inherent risk|inherent risks]] exist. Incidental risks are those that occur naturally in the business but are not part of the core of the business. Inherent risks have a negative effect on the operating profit of the business.

===In human services===
The experience of many people who rely on human services for support is that 'risk' is often used as a reason to prevent them from gaining further independence or fully accessing the community, and that these services are often unnecessarily risk averse.<ref>A Positive Approach To Risk Requires Person Centred Thinking, Neill et al., Tizard Learning Disability Review http://pierprofessional.metapress.com/content/vr700311x66j0125/</ref> "People's autonomy used to be compromised by institution walls, now it's too often our risk management practices", according to John O'Brien.<ref>John O'Brien cited in Sanderson, H. Lewis, J. A Practical Guide to Delivering Personalisation; Person Centred Practice in Health and Social Care p211</ref> Michael Fischer and Ewan Ferlie (2013) find that contradictions between formal risk controls and the role of subjective factors in human services (such as the role of emotions and ideology) can undermine service values, so producing tensions and even intractable and 'heated' conflict.<ref>{{cite journal|last=Fischer|first=Michael Daniel|author2=Ferlie, Ewan |title=Resisting hybridisation between modes of clinical risk management: Contradiction, contest, and the production of intractable conflict|journal=Accounting, Organizations and Society|date=1 January 2013|volume=38|issue=1|pages=30–49|doi=10.1016/j.aos.2012.11.002}}</ref>

===High reliability organizations (HROs)===
A [[Wikipedia:high reliability organization|high reliability organization]] (HRO) is an organization that has succeeded in avoiding catastrophes in an environment where [[Wikipedia:normal accidents|normal accidents]] can be expected due to risk factors and [[Wikipedia:Complex system|complexity]]].  Most studies of HROs involve areas such as nuclear aircraft carriers, air traffic control, aerospace and nuclear power stations. Organizations such as these share in common the ability to consistently operate safely in complex, interconnected environments where a single failure in one component could lead to catastrophe. Essentially, they are organizations which appear to operate 'in spite' of an enormous range of risks.

Some of these industries manage risk in a highly quantified and enumerated way. These include the [[Wikipedia:nuclear power|nuclear power]] and [[Wikipedia:Aerospace manufacturer|aircraft industries]], where the possible failure of a complex series of engineered systems could result in highly undesirable outcomes. The usual measure of risk for a class of events is then: ''R'' = probability of the event × the severity of the consequence.

The total risk is then the sum of the individual class-risks;  see below.{{Citation needed|reason=A previous version of this said, "product of ... class-risks".  This conflicted with, e.g., the formula below|date=August 2013}}

In the nuclear industry, consequence is often measured in terms of off-site radiological release, and this is often banded into five or six decade-wide bands.{{Clarify|reason=define "decade-wide bands":  factor of 10 regarding what?|date=August 2013}}

The risks are evaluated using fault tree/event tree techniques (see [[Wikipedia:safety engineering|safety engineering]]). Where these risks are low, they are normally considered to be "broadly acceptable". A higher level of risk (typically up to 10 to 100 times what is considered broadly acceptable) has to be justified against the costs of reducing it further and the possible benefits that make it tolerable—these risks are described as "Tolerable if [[Wikipedia:ALARP|ALARP]]". Risks beyond this level are classified as "intolerable".

The level of risk deemed broadly acceptable has been considered by regulatory bodies in various countries—an early attempt by UK government regulator and academic [[Wikipedia:F. R. Farmer|F. R. Farmer]] used the example of hill-walking and similar activities, which have definable risks that people appear to find acceptable. This resulted in the so-called Farmer Curve of acceptable probability of an event versus its consequence.

The technique as a whole is usually referred to as probabilistic risk assessment (PRA) (or probabilistic safety assessment, PSA). See [[Wikipedia:WASH-1400|WASH-1400]] for an example of this approach.

===Finance===
[[Wikipedia:Financial Risk|Main article Financial risk]]

In [[Wikipedia:finance|finance]], risk is the chance that the return achieved on an investment will be different from that expected, and also takes into account the size of the difference. This includes the possibility of losing some or all of the original investment. In a view advocated by Damodaran, risk includes not only "[[Wikipedia:downside risk|downside risk]]" but also "upside risk" (returns that exceed expectations).<ref>{{cite book |title=Investment Philosophies: Successful Investment Philosophies and the Greatest Investors Who Made Them Work |first=Aswath |last=Damodaran |page=15 |publisher=Wiley |year=2003 |isbn=0-471-34503-2}}</ref> Some regard the [[standard deviation]] of the historical returns or average returns of a specific investment as providing some historical measure of risk; see modern portfolio theory. Financial risk may be market-dependent, determined by numerous market factors, or operational, resulting from fraudulent behavior (e.g. [[Wikipedia:Bernard|Madoff Bernard Madoff]]). Recent studies suggest that endocrine levels may play a role in risk-taking in financial decision-making.<ref>Sapienza P., Zingales L. and Maestripieri D. 2009. Gender differences in financial risk aversion and career choices are affected by testosterone. Proceedings of the National Academy of Sciences.</ref><ref>Apicella C. L. and all.  Testosterone and financial risk preferences. Evolution and Human Behavior. vol 29. Issue 6. 384–390.[http://www.ehbonline.org/article/S1090-5138%2808%2900067-6/abstract abstract].</ref>

A fundamental idea in finance is the relationship between risk and return (see [[Wikipedia:modern portfolio theory|modern portfolio theory]]). The greater the potential return one might seek, the greater the risk that one generally assumes. A free market reflects this principle in the pricing of an instrument: strong demand for a safer instrument drives its price higher (and its return correspondingly lower) while weak demand for a riskier instrument drives its price lower (and its potential return thereby higher). For example, a US Treasury bond is considered to be one of the safest investments. In comparison to an investment or speculative grade corporate bond, US Treasury notes and bonds yield lower rates of return. The reason for this is that a corporation is more likely to default on debt than the U.S. government. Because the risk of investing in a corporate bond is higher, investors are offered a correspondingly higher rate of return.

A popular [[Wikipedia:risk|measure risk measure]] is [[Wikipedia:Value-at-Risk|value-at-risk]] (VaR).

There are different types of VaR: long term VaR, marginal VaR, factor VaR and shock VaR. The latter is used in measuring risk during the extreme market stress conditions.

In finance, ''risk'' has no single definition.

Artzner et al.<ref>Artzner P., Delbaen F., Eber J.-M., Heath D. 1999. Coherent measures of risk. Math. Finance, vol. 9, 203--228.</ref> write "we call risk the investor's future net worth". In Novak <ref>Novak S.Y. 2011. Extreme value methods with applications to finance. London: CRC. {{ISBN|978-1-43983-574-6}}.</ref> "risk is a possibility of an undesirable event".

In financial markets, one may need to measure [[Wikipedia:credit risk|credit risk]], information timing and source risk, probability model risk, operational risk and [[Wikipedia:legal risk|legal risk]] if there are regulatory or civil actions taken as a result of "[[Wikipedia:investor's regret|investor's regret]]".

With the advent of automation in financial markets, the concept of "real-time risk" has gained a lot of attention.  Aldridge and Krawciw<ref>Aldridge, I., Krawciw, S., 2017. Real-Time Risk: What Investors Should Know About Fintech, High-Frequency Trading and Flash Crashes. Hoboken: Wiley. {{ISBN|978-1119318965}}.</ref> define real-time risk as the probability of instantaneous or near-instantaneous loss, and can be due to flash crashes, other market crises, malicious activity by selected market participants and other events.  A well-cited example<ref>http://www.reuters.com/article/us-knightcapital-results-idUSBRE89G0HI20121017</ref> of real-time risk was a US $440 million loss incurred within 30 minutes by Knight Capital Group (KCG) on August 1, 2012; the culprit was a poorly-tested runaway algorithm deployed by the firm. Regulators have taken notice of real-time risk as well.  Basel III<ref>http://www.bis.org/bcbs/basel3.htm</ref> requires real-time risk management framework for bank stability.

It is not always obvious if [[Wikipedia:financial instruments|financial instruments]] are "[[Wikipedia:Hedge (finance)|hedging]]]" (purchasing/selling a financial instrument specifically to reduce or cancel out the risk in another investment) or "[[Wikipedia:speculation|speculation]]" (increasing measurable risk and exposing the investor to catastrophic loss in pursuit of very high windfalls that increase expected value).

Some people may be "[[Wikipedia:risk seeking|risk seeking]]]", i.e. their [[Wikipedia:utility function|utility function's]]] second derivative is positive. Such an individual willingly pays a premium to assume risk (e.g. buys a lottery ticket).

=== {{anchor|Risk in auditing}} Financial auditing ===
{{Main article|Audit risk}}
The [[audit risk|financial audit risk model]] expresses the risk of an [[auditor]] providing an inappropriate opinion (or material misstatement) of a commercial entity's financial statements. It can be analytically expressed as 
:<math> \text{AR} = \text{IR} \times \text{CR} \times \text{DR}</math>
where AR is ''audit risk'', IR is ''[[Inherent risk (accounting)|inherent risk]]'', CR is ''control risk'' and DR is ''detection risk''.

Note: As defined, audit risk does not consider the impact of an auditor misstatement and so is stated as a simple probability. The impact of misstatement must be considered when determining an acceptable audit risk.<ref>{{cite book|title = Risk Management and Corporate Governance: Interconnections in Law: Chapter: Risk Management from an accounting perspective | author = Arco van de Ven |pages = 16–17 |editors = Marijn van Daelen, Christoph van der Elst }}</ref>

===Security===
[[File:AT YOUR OWN RISK.svg|thumb|166px|'''AT YOUR OWN RISK'''<br />Popular labeling]]
Security risk management involves protection of assets from harm caused by deliberate acts. A more detailed definition is: "A security risk is any event that could result in the compromise of organizational assets i.e. the unauthorized use, loss, damage, disclosure or modification of organizational assets for the profit, personal interest or political interests of individuals, groups or other entities constitutes a compromise of the asset, and includes the risk of harm to people. Compromise of organizational assets may adversely affect the enterprise, its business units and their clients. As such, consideration of security risk is a vital component of risk management."<ref>Julian Talbot and Miles Jakeman ''Security Risk Management Body of Knowledge'', John Wiley & Sons, 2009.</ref>

===Human factors===
[[Wikipedia:Prospect theory|Main article: Decision theory}}
One of the growing areas of focus in risk management is the field of [[Wikipedia:human|factors human factors]]] where behavioral and organizational psychology underpin our understanding of risk based decision making. This field considers questions such as "how do we make risk based decisions?", "why are we irrationally more scared of sharks and terrorists than we are of motor vehicles and medications?"

In [[Wikipedia:decision theory|decision theory]], regret (and anticipation of regret) can play a significant part in decision-making, distinct from [[Wikipedia:risk aversion|risk aversion]]<ref>Virine, L., & Trumper, M. ProjectThink. Gower. 2013</ref> (preferring the status quo in case one becomes worse off).

[[Wikipedia:Framing (social sciences)|Framing]]<ref>Amos Tversky / Daniel Kahneman, 1981. "The Framing of Decisions and the Psychology of Choice."{{Verify source|date=October 2008}}</ref> is a fundamental problem with all forms of risk assessment. In particular, because of [[Wikipedia:bounded rationality|bounded rationality]] (our brains get overloaded, so we take mental shortcuts), the risk of extreme events is discounted because the probability is too low to evaluate intuitively. As an example, one of the leading causes of death is [[road accident]]s caused by [[Wikipedia:Driving under the influence|drunk driving]] – partly because any given driver frames the problem by largely or totally ignoring the risk of a serious or fatal accident.

For instance, an extremely disturbing event (an attack by hijacking, or [[Wikipedia:moral hazard|moral hazards]]) may be ignored in analysis despite the fact it has occurred and has a nonzero probability. Or, an event that everyone agrees is inevitable may be ruled out of analysis due to greed or an unwillingness to admit that it is believed to be inevitable. These human tendencies for error and [[Wikipedia:wishful thinking|wishful thinking]] often affect even the most rigorous applications of the [[Wikipedia:scientific method|scientific method]] and are a major concern of the [[Wikipedia:philosophy of science|philosophy of science]].

All [[Wikipedia:Decision|theory#Choice under uncertainty decision-making under uncertainty]] must consider [[Wikipedia:cognitive bias|cognitive bias]], [[Wikipedia:cultural bias|cultural bias]], and notational bias: No group of people assessing risk is immune to "[[Wikipedia:groupthink|groupthink]]": acceptance of obviously wrong answers simply because it is socially painful to disagree, where there are [[Wikipedia:conflict of interest|conflicts of interest]].

Framing involves other information that affects the outcome of a risky decision.  The right prefrontal cortex has been shown to take a more global perspective<ref>Schatz, J., Craft, S., Koby, M., & DeBaun, M. R. (2004).  Asymmetries in visual-spatial processing following childhood stroke.  Neuropsychology, 18, 340–352.</ref> while greater left prefrontal activity relates to local or focal processing.<ref>Volberg, G., & Hubner, R. (2004).  On the role of response conflicts and stimulus position for hemispheric differences in global/local processing: An ERP study.  Neuropsychologia, 42, 1805–1813.</ref>

From the Theory of Leaky Modules<ref>Drake, R. A. (2004).  Selective potentiation of proximal processes: Neurobiological mechanisms for spread of activation.  Medical Science Monitor, 10, 231–234.</ref> McElroy and Seta proposed that they could predictably alter the framing effect by the selective manipulation of regional prefrontal activity with finger tapping or monaural listening.<ref>McElroy, T., & Seta, J. J. (2004).  On the other hand, am I rational? Hemisphere activation and the framing effect.  Brain and Cognition, 55, 572–580.</ref>  The result was as expected.  Rightward tapping or listening had the effect of narrowing attention such that the frame was ignored.  This is a practical way of manipulating regional cortical activation to affect risky decisions, especially because directed tapping or listening is easily done.

===Psychology of risk taking===

A growing area of research has been to examine various psychological aspects of risk taking. Researchers typically run randomized experiments with a treatment and control group to ascertain the effect of different psychological factors that may be associated with risk taking. Thus, positive and negative feedback about past risk taking can affect future risk taking. In an experiment, people who were led to believe they are very competent at decision making saw more opportunities in a risky choice and took more risks, while those led to believe they were not very competent saw more threats and took fewer risks.<ref>Krueger, Norris, and Peter R. Dickson. "How believing in ourselves increases risk taking: perceived self-efficacy and opportunity recognition." Decision Sciences 25, no. 3 (1994): 385-400.</ref>

===Maintenance===
The concept of risk-based maintenance is an advanced form of [[Reliability centered maintenance]]. In case of chemical industries, apart from probability of failure, consequences of failure is also very important. Therefore, the selection of maintenance policies should be based on risk, instead of reliability. Risk-based maintenance methodology acts as a tool for maintenance planning and decision making to reduce the probability of failure and its consequences. In risk-based maintenance decision making, the maintenance resources can be utilized optimally based on the risk class (high, medium, or low) of equipment or machines, to achieve tolerable risk criteria.<ref>[http://www.sciencedirect.com/science/article/pii/S0304389406007345].</ref>

==Risk assessment and analysis==
{{Main article|Risk assessment|Operational risk management}}
Since risk assessment and management is essential in security management, both are tightly related. Security assessment methodologies like [[CRAMM]] contain risk assessment modules as an important part of the first steps of the methodology. On the other hand, risk assessment methodologies like [[Mehari]] evolved to become security assessment methodologies.
An [[International Organization for Standardization|ISO]] standard on risk management (Principles and guidelines on implementation) was published under code [[ISO 31000]] on 13 November 2009.

===Quantitative analysis===
There are many formal methods used to "measure" risk.

Often the probability of a negative event is estimated by using the frequency of past similar events. Probabilities for rare failures may be difficult to estimate. This makes risk assessment difficult in hazardous industries, for example nuclear energy, where the frequency of failures is rare, while harmful consequences of failure are severe.

Statistical methods may also require the use of a [[Loss function|cost function]], which in turn may require the calculation of the cost of loss of a human life. This is a difficult problem. One approach is to ask what people are willing to pay to insure against death<ref>{{Cite news|first = Steven|last = Landsburg|title = Is your life worth $10 million?|url = http://www.slate.com/id/2079475/|work = Everyday Economics|publisher = Slate|date = 2003-03-03|accessdate = 2008-03-17}}</ref> or radiological release (e.g. GBq of radio-iodine), {{Citation needed|date=March 2012}} but as the answers depend very strongly on the circumstances it is not clear that this approach is effective.

Risk is often measured as the [[expected value]] of an undesirable outcome. This combines the probabilities of various possible events and some assessment of the corresponding harm into a single value. See also [[Expected utility]].  The simplest case is a binary possibility of ''Accident'' or ''No accident''. The associated formula for calculating risk is then:

:<math> \text{R} = (\text{probability of the accident occurring}) \times  (\text{expected loss in case of the accident})</math>

For example, if performing activity ''X'' has a probability of 0.01 of suffering an accident of ''A'', with a loss of 1000, then total risk is a loss of 10, the product of 0.01 and 1000.

Situations are sometimes more complex than the simple binary possibility case. In a situation with several possible accidents, total risk is the sum of the risks for each different accident, provided that the outcomes are comparable:

:<math> \text{R} =  \sum_\text{For all accidents} (\text{probability of the accident occurring}) \times  (\text{expected loss in case of the accident})</math>

For example, if performing activity ''X'' has a probability of 0.01 of suffering an accident of ''A'', with a loss of 1000, and a probability of 0.000001 of suffering an accident of type ''B'', with a loss of 2,000,000, then total loss expectancy is 12, which is equal to a loss of 10 from an accident of type ''A'' and 2 from an accident of type ''B''.

One of the first major uses of this concept was for the planning of the [[Delta Works]] in 1953, a flood protection program in the [[Netherlands]], with the aid of the mathematician [[David van Dantzig]].<ref>[[Wired Magazine]], [https://www.wired.com/science/planetearth/magazine/17-01/ff_dutch_delta?currentPage=3 Before the levees break], page 3.</ref> The kind of risk analysis pioneered there has become common today in fields like nuclear power, [[aerospace]] and the [[chemical industry]].

In statistical decision theory, the [[risk function]] is defined as the expected value of a given [[loss function]] as a function of the [[decision rule]] used to make decisions in the face of uncertainty.

===Fear as intuitive risk assessment===
People may rely on their [[fear processing in the brain|fear]] and hesitation to keep them out of the most profoundly unknown circumstances. Fear is a response to perceived danger. Risk could be said to be the way we collectively measure and share this "true fear"—a fusion of rational doubt, irrational fear, and a set of unquantified biases from our own experience.

The field of [[behavioral finance]] focuses on human risk-aversion, asymmetric regret, and other ways that human financial behavior varies from what analysts call "rational". Risk in that case is the degree of [[uncertainty]] associated with a [[return (finance)|return]] on an asset.  Recognizing and respecting the irrational influences on human decision making may do much to reduce disasters caused by naive risk assessments that presume rationality but in fact merely fuse many shared biases.

==Anxiety, risk and decision making==

===Fear, anxiety and risk===
According to one set of definitions, fear is a fleeting emotion ascribed to a particular object, while [[anxiety]] is a trait of fear (this is referring to "trait anxiety", as distinct from how the term "anxiety" is generally used) that lasts longer and is not attributed to a specific stimulus (these particular definitions are not used by all authors cited on this page).<ref>Catherine A. Hartley, Elizabeth A. Phelps, Anxiety and Decision-Making, Biological Psychiatry, Volume 72, Issue 2, 15 July 2012, pp. 113–118, {{ISSN|0006-3223}}, 10.1016/j.biopsych.2011.12.027.</ref>  Some studies show a link between anxious behavior and risk (the chance that an outcome will have an unfavorable result).<ref>Jon Gertner. What Are We Afraid Of, Money 32.5 (2003): 80.</ref>   Joseph Forgas introduced [[valence (psychology)|valence]] based research where emotions are grouped as either positive or negative (Lerner and Keltner, 2000). Positive emotions, such as happiness, are believed to have more optimistic risk assessments and negative emotions, such as anger, have pessimistic risk assessments.  As an emotion with a negative valence, fear, and therefore anxiety, has long been associated with negative risk perceptions.  Under the more recent appraisal tendency framework of Jennifer Lerner et al., which refutes Forgas’ notion of valence and promotes the idea that specific emotions have distinctive influences on judgments, fear is still related to pessimistic expectations.<ref>Jennifer S. Lerner, Dacher Keltner. Beyond Valence: Toward A Model of Emotion-Specific Influences on Judgment and Choice. Cognition & Emotion 14.4 (2000): 473–493.</ref>

Psychologists have demonstrated that increases in anxiety and increases in [[Risk_Literacy|risk perception]] are related and people who are habituated to anxiety experience this awareness of risk more intensely than normal individuals.<ref name="Jon">Jon K. Maner, Norman B. Schmidt, The Role of Risk Avoidance in Anxiety, Behavior Therapy, Volume 37, Issue 2, June 2006, pp. 181–189, {{ISSN|0005-7894}}, 10.1016/j.beth.2005.11.003.</ref>   In decision-making, anxiety promotes the use of biases and quick thinking to evaluate risk.  This is referred to as affect-as-information according to Clore, 1983.  However, the accuracy of these risk perceptions when making choices is not known.<ref name="Joseph">Joseph I. Constans, Worry propensity and the perception of risk, Behaviour Research and Therapy, Volume 39, Issue 6, June 2001, pp. 721–729, {{ISSN|0005-7967}}, 10.1016/S0005-7967(00)00037-1.</ref>

=== Consequences of anxiety ===
Experimental studies show that brief surges in anxiety are correlated with surges in general risk perception.<ref name="Joseph" />   Anxiety exists when the presence of threat is perceived (Maner and Schmidt, 2006).<ref name="Jon" />   As risk perception increases, it stays related to the particular source impacting the mood change as opposed to spreading to unrelated risk factors.<ref name="Joseph" />   This increased awareness of a threat is significantly more emphasized in people who are conditioned to anxiety.<ref name="Jon_a">Jon K. Maner, J. Anthony Richey, Kiara Cromer, Mike Mallott, Carl W. Lejuez, Thomas E. Joiner, Norman B. Schmidt, Dispositional anxiety and risk-avoidant decision-making, Personality and Individual Differences, Volume 42, Issue 4, March 2007, pp. 665–675, {{ISSN|0191-8869}}, 10.1016/j.paid.2006.08.016.</ref>   For example, anxious individuals who are predisposed to generating reasons for negative results tend to exhibit pessimism.<ref name="Jon_a" />    Also, findings suggest that the perception of a lack of control and a lower inclination to participate in risky decision-making (across various behavioral circumstances) is associated with individuals experiencing relatively high levels of trait anxiety.<ref name="Jon" />   In the previous instance, there is supporting clinical research that links emotional evaluation (of control), the anxiety that is felt and the option of risk avoidance.<ref name="Jon" />

There are various views presented that anxious/fearful emotions cause people to access involuntary responses and judgments when making decisions that involve risk.  Joshua A. Hemmerich et al. probes deeper into anxiety and its impact on choices by exploring "risk-as-feelings" which are quick, automatic, and natural reactions to danger that are based on emotions.  This notion is supported by an experiment that engages physicians in a simulated perilous surgical procedure.  It was demonstrated that a measurable amount of the participants' anxiety about patient outcomes was related to previous (experimentally created) regret and worry and ultimately caused the physicians to be led by their feelings over any information or guidelines provided during the mock surgery.  Additionally, their emotional levels, adjusted along with the simulated patient status, suggest that anxiety level and the respective decision made are correlated with the type of bad outcome that was experienced in the earlier part of the experiment.<ref>Joshua A. Hemmerich, Arthur S. Elstein, Margaret L. Schwarze, Elizabeth Ghini Moliski, William Dale, Risk as feelings in the effect of patient outcomes on physicians' future treatment decisions: A randomized trial and manipulation validation, Social Science &amp; Medicine, Volume 75, Issue 2, July 2012, pp. 367–376, {{ISSN|0277-9536}}, 10.1016/j.socscimed.2012.03.020.</ref>  Similarly, another view of anxiety and decision-making is dispositional anxiety where emotional states, or [[mood (psychology)|moods]], are cognitive and provide information about future pitfalls and rewards (Maner and Schmidt, 2006).  When experiencing anxiety, individuals draw from personal judgments referred to as pessimistic outcome appraisals.  These emotions promote biases for risk avoidance and promote risk tolerance in decision-making.<ref name="Jon_a" />

===Dread risk===
It is common for people to dread some risks but not others: They tend to be very afraid of epidemic diseases, nuclear power plant failures, and plane accidents but are relatively unconcerned about some highly frequent and deadly events, such as traffic crashes, household accidents, and medical errors. One key distinction of dreadful risks seems to be their potential for catastrophic consequences,<ref name="Slovic P 1987">Slovic P (1987) Perception of risk. Science 236:280−285.</ref> threatening to kill a large number of people within a short period of time.<ref>Gigerenzer G (2004) Dread risk, September 11, and fatal traffic accidents. Psych Sci 15:286−287.</ref> For example, immediately after the September 11 attacks, many Americans were afraid to fly and took their car instead, a decision that led to a significant increase in the number of fatal crashes in the time period following the 9/11 event compared with the same time period before the attacks.<ref>Gaissmaier, W., & Gigerenzer, G. (2012). 9/11, Act II: A fine-grained analysis of regional variations in traffic fatalities in the aftermath of the terrorist attacks. Psychological Science, 23, 1449–1454.</ref><ref name="Lichtenstein S 1978">Lichtenstein S, Slovic P, Fischhoff B, Layman M, Combs B (1978) Judged frequency of lethal events. J Exp Psych HLM 4:551–578.</ref>

Different hypotheses have been proposed to explain why people fear dread risks. First, the psychometric paradigm<ref name="Slovic P 1987"/> suggests that high lack of control, high catastrophic potential, and severe consequences account for the increased risk perception and anxiety associated with dread risks. Second, because people estimate the frequency of a risk by recalling instances of its occurrence from their social circle or the media, they may overvalue relatively rare but dramatic risks because of their overpresence and undervalue frequent, less dramatic risks.<ref name="Lichtenstein S 1978"/> Third, according to the preparedness hypothesis, people are prone to fear events that have been particularly threatening to survival in human evolutionary history.<ref>Öhman A, Mineka S (2001) Fears, phobias, and preparedness: Toward an evolved module of fear and fear learning. Psychol Rev 108:483–522.</ref> Given that in most of human evolutionary history people lived in relatively small groups, rarely exceeding 100 people,<ref>Hill KR, Walker RS, Bozicevic M, Eder J, Headland T et al. (2011) Co-residence patterns in hunter-gatherer societies show unique human social structure. Science 331:1286–1289.</ref> a dread risk, which kills many people at once, could potentially wipe out one’s whole group. Indeed, research found<ref>Galesic M, Garcia-Retamero, R (2012) The risks we dread: A social circle account. PLoS ONE 7(4): e32837.</ref> that people’s fear peaks for risks killing around 100 people but does not increase if larger groups are killed. Fourth, fearing dread risks can be an ecologically rational strategy.<ref>Bodemer, N., Ruggeri, A., & Galesic, M. (2013). When dread risks are more dreadful than continuous risks: Comparing cumulative population losses over time. PLoS One, 8, e66544.</ref> Besides killing a large number of people at a single point in time, dread risks reduce the number of children and young adults who would have potentially produced offspring. Accordingly, people are more concerned about risks killing younger, and hence more fertile, groups.<ref>Wang XT (1996) Evolutionary hypotheses of risk-sensitive choice: Age differences and perspective change. Ethol Sociobiol 17:1–15.</ref>

===Anxiety and judgmental accuracy===
The relationship between higher levels of risk perception and "judgmental accuracy" in anxious individuals remains unclear (Joseph I. Constans, 2001).  There is a chance that "judgmental accuracy" is correlated with heightened anxiety.  Constans conducted a study to examine how worry propensity (and current mood and trait anxiety) might influence college student’s estimation of their performance on an upcoming exam, and the study found that worry propensity predicted subjective risk bias (errors in their risk assessments), even after variance attributable to current mood and trait anxiety had been removed.<ref name="Joseph" />   Another experiment suggests that trait anxiety is associated with pessimistic risk appraisals (heightened perceptions of the probability and degree of suffering associated with a negative experience), while controlling for depression.<ref name="Jon" />

==Other considerations==
===Risk and uncertainty===
In his seminal work ''Risk, Uncertainty, and Profit'', [[Frank Knight]] (1921) established the distinction between risk and uncertainty.
{{quote|... Uncertainty must be taken in a sense radically distinct from the familiar notion of Risk, from which it has never been properly separated. The term "risk," as loosely used in everyday speech and in economic discussion, really covers two things which, functionally at least, in their causal relations to the phenomena of economic organization, are categorically different. ... The essential fact is that "risk" means in some cases a quantity susceptible of measurement, while at other times it is something distinctly not of this character; and there are far-reaching and crucial differences in the bearings of the phenomenon depending on which of the two is really present and operating. ... It will appear that a measurable uncertainty, or "risk" proper, as we shall use the term, is so far different from an unmeasurable one that it is not in effect an uncertainty at all. We ... accordingly restrict the term "uncertainty" to cases of the non-quantitive type.:<ref>Frank Hyneman Knight "Risk, uncertainty and profit" pg. 19, Hart, Schaffner, and Marx Prize Essays, no. 31. Boston and New York: Houghton Mifflin. 1921.</ref>}}

Thus, [[Knightian uncertainty]] is immeasurable, not possible to calculate, while in the Knightian sense risk is measurable.

Another distinction between risk and uncertainty is proposed by Douglas Hubbard:<ref>Douglas Hubbard "How to Measure Anything: Finding the Value of Intangibles in Business" pg. 46, John Wiley & Sons, 2007.</ref><ref name = "ReferenceA">Douglas Hubbard "The Failure of Risk Management: Why It's Broken and How to Fix It, John Wiley & Sons, 2009.</ref>

:'''Uncertainty''': The lack of complete certainty, that is, the existence of more than one possibility. The "true" outcome/state/result/value is not known.
:'''Measurement of uncertainty''': A set of probabilities assigned to a set of possibilities. Example: "There is a 60% chance this market will double in five years"
:'''Risk''': A state of uncertainty where some of the possibilities involve a loss, catastrophe, or other undesirable outcome.
:'''Measurement of risk''': A set of possibilities each with quantified probabilities and quantified losses. Example: "There is a 40% chance the proposed oil well will be dry with a loss of $12 million in exploratory drilling costs".

In this sense, one may have uncertainty without risk but not risk without uncertainty. We can be uncertain about the winner of a contest, but unless we have some personal stake in it, we have no risk. If we bet money on the outcome of the contest, then we have a risk. In both cases there are more than one outcome. The measure of uncertainty refers only to the probabilities assigned to outcomes, while the measure of risk requires both probabilities for outcomes and losses quantified for outcomes.

===Risk attitude, appetite and tolerance===
{{Main article|Risk aversion}}

The terms ''risk attitude'', ''appetite'', and ''tolerance'' are often used similarly to describe an organization's or individual's attitude towards risk-taking. One's attitude may be described as ''risk-averse'', ''risk-neutral'', or ''risk-seeking''. Risk tolerance looks at acceptable/unacceptable deviations from what is expected.{{unclear inline|date=May 2017}} Risk appetite looks at how much risk one is willing to accept. There can still be deviations that are within a risk appetite. For example, recent research finds that insured individuals are significantly likely to divest from risky asset holdings in response to a decline in health, controlling for variables such as income, age, and out-of-pocket medical expenses.<ref>[http://www.chicagofed.org/digital_assets/publications/working_papers/2009/wp2009_23.pdf Federal Reserve Bank of Chicago, ''Health and the Savings of Insured versus Uninsured, Working-Age Households in the U.S.'', November 2009]</ref>

[[Gambling]] is a risk-increasing investment, wherein money on hand is risked for a possible large return, but with the possibility of losing it all. Purchasing a lottery ticket is a very risky investment with a high chance of no return and a small chance of a very high return. In contrast, putting money in a bank at a defined rate of interest is a risk-averse action that gives a guaranteed return of a small gain and precludes other investments with possibly higher gain.  The possibility of getting no return on an investment is also known as the [[rate of ruin]].

===Risk as a vector quantity===
Hubbard also argues that defining risk as the product of impact and probability presumes, unrealistically, that decision-makers are [[risk-neutral]].<ref name = "ReferenceA"/>{{page number|date=May 2017}} A risk-neutral person's utility is proportional to the [[expected value]] of the payoff. For example, a risk-neutral person would consider 20% chance of winning $1 million exactly as desirable as getting a certain $200,000. However, most decision-makers are not actually risk-neutral and would not consider these equivalent choices. This gave rise to [[prospect theory]] and [[cumulative prospect theory]]. Hubbard proposes to instead describe risk as a [[Vector space|vector]] quantity that distinguishes the probability and magnitude of a risk. Risks are simply described as a set or function{{vague|date=May 2017}} of possible payoffs (gains or losses) with their associated probabilities. This array is collapsed into a scalar value according to a decision-maker's [[risk aversion|risk tolerance]].

== List of related books ==

This is a '''list of books about risk''' issues.

{| class="wikitable"
! Title
! Author(s)
! Year
|-
| ''Acceptable Risk'' || Baruch Fischhoff, Sarah Lichtenstein, [[Paul Slovic]], Steven L. Derby, and Ralph Keeney || 1984
|-
| ''Against the Gods: The Remarkable Story of Risk'' || [[Peter L. Bernstein]] || 1996
|-
| ''At risk: Natural hazards, people's vulnerability and disasters'' || [[Piers Blaikie]], Terry Cannon, Ian Davis, and Ben Wisner || 1994
|-
| ''[[Building Safer Communities. Risk Governance, Spatial Planning and Responses to Natural Hazards]]'' || Urbano Fra Paleo || 2009
|-
| ''Dangerous Earth: An introduction to geologic hazards'' || Barbara W. Murck, Brian J. Skinner, Stephen C. Porter ||1998
|-
| ''Disasters and Democracy'' || Rutherford H. Platt || 1999
|-
| ''Earth Shock: Hurricanes, volcanoes, earthquakes, tornadoes and other forces of nature'' || [[W. Andrew Robinson]] || 1993
|-
| ''Human System Response to Disaster: An Inventory of Sociological Findings'' || Thomas E. Drabek || 1986
|-
| ''Judgment Under Uncertainty: heuristics and biases'' || [[Daniel Kahneman]], [[Paul Slovic]], and [[Amos Tversky]] || 1982
|-
| ''Mapping Vulnerability: disasters, development, and people'' || Greg Bankoff, Georg Frerks, and Dorothea Hilhorst || 2004
|-
| ''Man and Society in Calamity: The Effects of War, Revolution, Famine, Pestilence upon Human Mind, Behavior, Social Organization and Cultural Life'' || [[Pitirim Sorokin]] || 1942
|-
| ''Mitigation of Hazardous Comets and Asteroids'' || Michael J.S. Belton, Thomas H. Morgan, Nalin H. Samarasinha, Donald K. Yeomans || 2005
|-
| ''Natural Disaster Hotspots: a global risk analysis''  || Maxx Dilley  || 2005
|-
| ''Natural Hazard Mitigation: Recasting disaster policy and planning'' || David Godschalk, [[Timothy Beatley]], Philip Berke, David Brower, and Edward J. Kaiser || 1999
|-
| ''Natural Hazards: Earth’s processes as hazards, disasters, and catastrophes'' || Edward A. Keller, and Robert H. Blodgett || 2006
|-
| ''Normal Accidents. Living with high-risk technologies'' || [[Charles Perrow]] || 1984
|-
| ''Paying the Price: The status and role of insurance against natural disasters in the United States'' || Howard Kunreuther, and Richard J. Roth || 1998
|-
| ''Planning for Earthquakes:  Risks, politics, and policy'' || Philip R. Berke, and Timothy Beatley || 1992
|-
| ''Practical Project Risk Management: The ATOM Methodology'' || David Hillson and Peter Simon || 2012
|-
| ''Reduction and Predictability of Natural Disasters'' || John B. Rundle, William Klein, Don L. Turcotte || 1996
|-
| ''Regions of Risk:  A geographical introduction to disasters'' || Kenneth Hewitt || 1997
|-
| ''Risk Analysis: a quantitative guide'' || David Vose || 2008
|-
| ''Risk: An introduction ({{ISBN|978-0-415-49089-4}})'' || Bernardus Ale || 2009
|-
| ''Risk and Culture: An essay on the selection of technical and environmental dangers'' || [[Mary Douglas]], and [[Aaron Wildavsky]] || 1982
|-
| ''Socially Responsible Engineering: Justice in Risk Management ({{ISBN|978-0-471-78707-5}})'' || [[Daniel A. Vallero]], and P. Aarne Vesilind || 2006
|-
| ''Swimming with Crocodiles: The Culture of Extreme Drinking'' 
| Marjana Martinic and Fiona Measham (eds.) 
| 2008
|-
| ''The Challenger Launch Decision: Risky Technology, Culture and Deviance at NASA'' || Diane Vaughan || 1997
|-
| ''The Environment as Hazard ''|| Ian Burton, [[Robert Kates]], and [[Gilbert F. White]] || 1978
|-
| ''The Social Amplification of Risk'' || Nick Pidgeon, Roger E. Kasperson, and [[Paul Slovic]] || 2003
|-
| ''What is a Disaster? New answers to old questions'' || Ronald W. Perry, and [[Enrico Quarantelli]] || 2005
|-
| ''Floods: From Risk to Opportunity ([[International Association of Hydrological Sciences|IAHS]] Red Book Series) '' || Ali Chavoshian, and Kuniyoshi Takeuchi || 2013
|-
| ''The Risk Factor: Why Every Organization Needs Big Bets, Bold Characters, and the Occasional Spectacular Failure'' || [[Deborah Perry Piscione]] || 2014
|}

==See also==
{{div col|colwidth=30em}}
* [[Ambiguity aversion]]
* [[Benefit shortfall]]
* [[Civil defense]]
* [[Countermeasure]]
* [[Early case assessment]]
* [[Event chain methodology]]
* [[Fuel price risk management]]
* [[Global catastrophic risk]]
* [[Global Risk Forum GRF Davos]]
* [[Hazard (risk)]]
* [[Identity resolution]]
* [[Information assurance]]
* [[Inherent risk]]
* [[Inherent risk (accounting)]]
* [[International Risk Governance Council]]
* [[ISO/PAS 28000]]
* [[Life-critical system]]
* [[Loss aversion]]
* [[Preventive maintenance]]
* [[Probabilistic risk assessment]]
* [[Reputational risk]]
* [[Reliability engineering]]
* [[Risk analysis (business)|Risk analysis]]
* [[Risk compensation]]
** [[Peltzman effect]]
* [[Risk management]]
* [[Risk-neutral measure]]
* [[Risk register]]
* [[Sampling risk]]
* [[Vulnerability]]
{{div col end}}

==References==
{{Reflist|30em}}

==Bibliography==

===Referred literature===
* [[James Franklin (philosopher)|James Franklin]], 2001: ''The Science of Conjecture: Evidence and Probability Before Pascal'', Baltimore: Johns Hopkins University Press.
* {{Cite journal | year= 2005 | authors= John Handmer and [[Paul James (academic)|Paul James]] | title=Trust Us and Be Scared: The Changing Nature of Risk | url= https://www.academia.edu/3791859/Trust_Us_and_Be_Scared_The_Changing_Nature_of_Contemporary_Risk | journal= Global Society | volume= 21 | issue=  1 | pages= 119–30.}} 
* [[Niklas Luhmann]], 1996: ''Modern Society Shocked by its Risks'' (= University of Hong Kong, Department of Sociology Occasional Papers 17), Hong Kong, available via [http://hub.hku.hk/handle/10722/42552 HKU Scholars HUB]

===Books===
* Historian [[David A. Moss]]' book [http://www.hup.harvard.edu/catalog/MOSWHE.html ''When All Else Fails''] explains the [[U.S. government]]'s historical role as risk manager of last resort.
* Bernstein P. L. ''Against the Gods'' {{ISBN|0-471-29563-9}}. Risk explained and its appreciation by man traced from earliest times through all the major figures of their ages in mathematical circles.
* {{Cite book|last = Rescher|first = Nicholas|title = A Philosophical Introduction to the Theory of Risk Evaluation and Measurement|publisher = University Press of America|year = 1983}}
* {{Cite book|last = Porteous|first = Bruce T.|author2=Pradip Tapadar |title = Economic Capital and Financial Risk Management for Financial Services Firms and Conglomerates|publisher = Palgrave Macmillan|date=December 2005|isbn = 1-4039-3608-0}}
* {{Cite book|author = Tom Kendrick|year = 2003|title = Identifying and Managing Project Risk: Essential Tools for Failure-Proofing Your Project|publisher = AMACOM/American Management Association|isbn = 978-0-8144-0761-5}}
* {{Cite book|author = Hillson D. |year = 2007|title = Practical Project Risk Management: The Atom Methodology|publisher = Management Concepts|isbn = 978-1-56726-202-5}}
* {{Cite book|author = Kim Heldman|year = 2005|title = Project Manager's Spotlight on Risk Management|publisher = Jossey-Bass|isbn = 978-0-7821-4411-6}}
* {{Cite book|author = Dirk Proske|year = 2008|title = Catalogue of risks – Natural, Technical, Social and Health Risks|publisher = Springer|isbn = 978-3-540-79554-4}}
* Gardner D. [https://books.google.com/books?id=5j_8xF8vUlAC&printsec=frontcover ''Risk: The Science and Politics of Fear''], Random House Inc. (2008) {{ISBN|0-7710-3299-4}}.
* Novak S.Y. Extreme value methods with applications to finance. London: CRC. (2011) {{ISBN|978-1-43983-574-6}}. 
* Hopkin P. Fundamentals of Risk Management. 2nd Edition. Kogan-Page (2012) {{ISBN|978-0-7494-6539-1}}

===Articles and papers===
* Cevolini, A. (2015). "Tempo e decisione. Perché Aristotele non ha un concetto di rischio?" [https://www.academia.edu/14281713/Tempo_e_decisione._Perch%C3%A9_Aristotele_non_ha_un_concetto_di_rischio] ''Divus Thomas'', 118 (1), 221-249.
* Clark, L., Manes, F., Antoun, N., [[Barbara Sahakian|Sahakian, B. J.]], & Robbins, T. W. (2003). "The contributions of lesion laterality and lesion volume to decision-making impairment following frontal lobe damage." ''Neuropsychologia'', 41, 1474–1483.
* Cokely, E. T., Galesic, M., Schulz, E., Ghazal, S., & Garcia-Retamero, R. (2012). [http://journal.sjdm.org/11/11808/jdm11808.pdf Measuring risk literacy: The Berlin Numeracy Test.] ''Judgment and Decision Making, 7,'' 25–47.
* Drake, R. A. (1985). "Decision making and risk taking: Neurological manipulation with a proposed consistency mediation." ''Contemporary Social Psychology, 11,'' 149–152.
* Drake, R. A. (1985). "Lateral asymmetry of risky recommendations." ''Personality and Social Psychology Bulletin, 11,'' 409–417.
* Gregory, Kent J., Bibbo, Giovanni and Pattison, John E. (2005), "A Standard Approach to Measurement Uncertainties for Scientists and Engineers in Medicine", ''Australasian Physical and Engineering Sciences in Medicine'' '''28'''(2):131–139.
* Hansson, Sven Ove. (2007). [http://plato.stanford.edu/entries/risk/ "Risk"], ''The Stanford Encyclopedia of Philosophy'' (Summer 2007 Edition), Edward N. Zalta (ed.), forthcoming [http://plato.stanford.edu/archives/sum2007/entries/risk/].
* Holton, Glyn A. (2004). [http://www.riskexpertise.com/papers/risk.pdf "Defining Risk"], ''Financial Analysts Journal'', 60 (6), 19–25. A paper exploring the foundations of risk. (PDF file).
* Knight, F. H. (1921) ''Risk, Uncertainty and Profit'', Chicago: Houghton Mifflin Company. (Cited at: [http://www.econlib.org/library/Knight/knRUP1.html], § I.I.26.).
* Kruger, Daniel J., Wang, X.T., & Wilke, Andreas (2007) [http://www.epjournal.net/filestore/ep05555568.pdf "Towards the development of an evolutionarily valid domain-specific risk-taking scale"] ''Evolutionary Psychology'' (PDF file).
* Metzner-Szigeth, A. (2009). "Contradictory Approaches? – On Realism and Constructivism in the Social Sciences Research on Risk, Technology and the Environment." ''Futures'', Vol. 41, No. 2, March 2009, pp.&nbsp;156–170 (fulltext journal: [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V65-4TGS7JY-1&_user=10&_coverDate=04%2F30%2F2009&_rdoc=1&_fmt=high&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=054fec1f03e9ec784596add85197d2a8]) (free preprint: [http://dx.doi.org/10.6084/m9.figshare.1174661]).
* Miller, L. (1985). "Cognitive risk taking after frontal or temporal lobectomy I. The synthesis of fragmented visual information."  ''Neuropsychologia'', 23, 359–369.
* Miller, L., & Milner, B. (1985). "Cognitive risk taking after frontal or temporal lobectomy II. The synthesis of phonemic and semantic information." ''Neuropsychologia'', 23, 371–379.
* Neill, M. Allen, J. Woodhead, N. Reid, S. Irwin, L. Sanderson, H. 2008 "A Positive Approach to Risk Requires Person Centred Thinking" London, CSIP Personalisation Network, Department of Health. Available from: http://networks.csip.org.uk/Personalisation/Topics/Browse/Risk/ [Accessed 21 July 2008].
* {{cite encyclopedia |last1=Wildavsky|first1=Aaron |authorlink1=Aaron Wildavsky|last2=Wildavsky|first2=Adam|editor=[[David R. Henderson]] |encyclopedia=[[Concise Encyclopedia of Economics]] |title=Risk and Safety |url=http://www.econlib.org/library/Enc/RiskandSafety.html  |year=2008 |edition= 2nd |publisher=[[Library of Economics and Liberty]] |location=Indianapolis |isbn=978-0865976658 |oclc=237794267}}

==External links==
{{Sisterlinks|Risk}}
* [http://plato.stanford.edu/entries/risk/ Risk] – The entry of the Stanford Encyclopedia of Philosophy

{{Environmental social science|state=collapsed}}
{{Use dmy dates|dat e=September 2010|date=April 2017}}

{{Authority control}}

{{DEFAULTSORT:Risk}}
[[Category:Risk| ]]
[[Category:Actuarial science]]
[[Category:Financial risk]]
[[Category:Environmental social science concepts]]