In mathematical finance, the Greeks are the quantities representing the sensitivity of the price of derivatives such as options to a change in underlying parameters on which the value of an instrument or portfolio of financial instruments is dependent. The name is used because the most common of these sensitivities are denoted by Greek letters (as are some other finance measures). Collectively these have also been called the risk sensitivities,risk measures or hedge parameters.
The Greeks are vital tools in risk management. Each Greek measures the sensitivity of the value of a portfolio to a small change in a given underlying parameter, so that component risks may be treated in isolation, and the portfolio rebalanced accordingly to achieve a desired exposure; see for example delta hedging.
The Greeks in the Black–Scholes model are relatively easy to calculate, a desirable property of financial models, and are very useful for derivatives traders, especially those who seek to hedge their portfolios from adverse changes in market conditions. For this reason, those Greeks which are particularly useful for hedging—such as delta, theta, and vega—are well-defined for measuring changes in Price, Time and Volatility. Although rho is a primary input into the Black–Scholes model, the overall impact on the value of an option corresponding to changes in the risk-free interest rate is generally insignificant and therefore higher-order derivatives involving the risk-free interest rate are not common.
Color is the second EP by Japanese visual kei band, Girugamesh, released on July 7, 2010.
Color (stylized as COLOR) was a Japanese punk band formed in 1985 by Dynamite Tommy, who founded the Free-Will record label a year later. They are considered to be important to the formation of visual kei. Their debut album Gekitotsu was named one of the top albums from 1989-1998 in a 2004 issue of the music magazine Band Yarouze.
Color released their debut album Gekitotsu, in January 1988. After releasing their second album Fools! Get Lucky!!, they signed to Crown Records and released their only major studio album a couple months later, Ask the Angels. It is said that the label made the band rewrite the album's lyrics, which were originally in English, in Japanese to be more accessible by the mainstream. It seemed to have worked, as Ask the Angels reached number 16 on the Oricon chart and their popularity increased. However, in January 1990 at a concert on the album's tour, in their hometown of Osaka, a fan was accidentally stomped to death. The band decided to lay low and avoid media, they ended up losing their contract with Crown. During this hiatus, Tommy formed Sister's No Future with Ken-chan (Kamaitachi), while Marry started Goatcore with You Adachi (Dead End).
Image is an original novel based on the U.S. television series Angel.
Cordelia Chase has a vision of a child being attacked by a squidlike demon. Meanwhile, Gunn is trying to rescue a young artist; the artist's studio is being attacked by vampires. Cordelia goes to investigate the mansion from her vision. She soon finds herself surrounded by baby products, portraits, and chased by a tentacled monster.
When Angel arrives on the scene, he is surprised to discover that he recognizes some of the portraits. He holds distant memories of him and Darla spending a night with storytellers and artists. Angel reveals that he and Darla were present at the party where Mary Shelley was inspired to write Frankenstein; indeed, they witnessed the event that gave Mary the initial idea.
An old evil is trying to use a painting to preserve the life of its body, which, in the terms of the story, inspired the novel The Picture of Dorian Gray. In their efforts to save a child the villain is focused on, Team Angel will learn not to judge everything by its image.
Image is an American quarterly literary journal that publishes art and writing engaging or grappling with Judeo-Christian faith. The journal's byline is Art, Faith, Mystery. Image features fiction, poetry, painting, sculpture, architecture, film, music, and dance. The journal also sponsors the Glen Workshops, the Arts & Faith discussion forum, the Milton Fellowship for writers working on their first book, the summer Luci Shaw Fellowship for undergrads, and the Denise Levertov Award.
Material first published in Image has appeared in Harper's Magazine, The Best American Essays, The Pushcart Prize: Best of the Small Presses, The Best Spiritual Writing, The O. Henry Prize Stories, The Art of the Essay, New Stories from the South, The Best American Movie Writing, and The Best Christian Writing. In 2000 and 2003, Image was nominated by Utne Reader for an Independent Press Award in the category of Spiritual Coverage.
Image was established in 1989 by Gregory Wolfe and is non-profit quarterly based at Seattle Pacific University.Image was involved with the founding of Seattle Pacific University’s Master of Fine Arts degree, which launched in 2005. The SPU MFA is the world’s first university-based low-residency MFA program to integrate writing and Christian conviction, guided by teachers such as Scott Cairns, Robert Clark, Paula Huston, Gina Ochsner, Jeanne Murray Walker, and Lauren Winner.
Given a category C and a morphism
in C, the image of f is a monomorphism
satisfying the following universal property:
Remarks:
The image of f is often denoted by im f or Im(f).
One can show that a morphism f is epic if and only if f = im f.
In the category of sets the image of a morphism is the inclusion from the ordinary image
to
. In many concrete categories such as groups, abelian groups and (left- or right) modules, the image of a morphism is the image of the correspondent morphism in the category of sets.
In any normal category with a zero object and kernels and cokernels for every morphism, the image of a morphism can be expressed as follows: