We survey some of the recent developments on quasi-Monte Carlo (QMC) methods, which,
in their basic form, are a deterministic counterpart to the Monte Carlo (MC) method. Our main …

This is a review article on lattice methods for multiple integration over the unit hypercube, with
a variance-reduction viewpoint. It also contains some new results and ideas. The aim is to …

Integration lattices are one of the main types of low discrepancy sets used in quasi-Monte
Carlo methods. However, they have the disadvantage of being of fixed size. This article …

Halton sequences have always been quite popular with practitioners, in part because of
their intuitive definition and ease of implementation. However, in their original form, these …

Optimal reinsurance from an insurer's point of view or from a reinsurer's point of view has been
studied extensively in the literature. However, as two parties of a reinsurance contract, an …

Discrepancy is a well-known measure for the irregularity of the distribution of a point set. Point
sets with small discrepancy are called low discrepancy and are known to efficiently fill the …

Quasi-Monte Carlo (QMC) methods have begun to displace ordinary Monte Carlo (MC)
methods in many practical problems. It is natural and obvious to combine QMC methods with …

In a reinsurance contract, a reinsurer promises to pay the part of the loss faced by an insurer
in exchange for receiving a reinsurance premium from the insurer. However, the reinsurer …

The Multiple-Try Metropolis is a recent extension of the Metropolis algorithm in which the
next state of the chain is selected among a set of proposals. We propose a modification of the …

The distribution of light in the canopy is a major factor regulating the growth and development
of a plant. The main variables of interest are the amount of photosynthetically active …