The conventional Monte Carlo approach to integration and simulation is a useful alternative to analytic or quadrature methods. It has been recognized through theory and practice that a variety of uniformly distributed sequences provide more accurate results than a purely pseudorandom sequence....

Two new second-order finite difference techniques based upon the classical 3-point backward time centered space (BTCS) method and the Crank–Nicolson scheme, and also a fourth-order finite difference scheme based on Crandall's method for one-dimensional diffusion, are used to solve the...

Using number-theoretic methods, we investigate low-discrepancy sequences and weighted-sum estimators which outperform standard low-discrepancy techniques for pricing multi-asset European options on up to 5 underlying factors. The sequences used are simpler to implement than most low-discrepancy...

Relations between Monte Carlo and quasi-Monte Carlo methods are analysed from both theoretical and practical points of view with special emphasis on high-dimensional integration.

It is well known that low-discrepancy sequences and their discrepancy play essential roles in quasi Monte Carlo methods [5]. In this paper, a new class of low-discrepancy sequences Nβ is constructed by using the ergodic theoretical transformation which is called β-adic transformation [7, 8]....

We show how the formal theory of differential equations provides a unifying framework for some aspects of constrained Hamiltonian systems and of the numerical analysis of differential algebraic equations, respectively. This concerns especially the Dirac algorithm for the construction of all...

Recent work in the development of stochastic methods for multiple integrals over unbounded regions is reviewed and generalized. This includes randomization or deterministic rules, and new stochastic rules for integrals with multivariate Normal weight. Stochastic spherical–radial rules are also...