A new, simple algorithm of order 2 is presented to approximate weakly stochastic differential equations. It is then applied to the problem of pricing Asian options under the Heston stochastic volatility model. 2000 Mathematics Subject Classification, 65C30, 65C05.

In contrast to random points that may cluster, quasi-random points keep their distance. These distances are investigated.1.If N independent random points in the n-dimensional unit hypercube are selected, two of these points may be arbitrarily close. However, if Q0, Q1, …, QN−1, are...

Integrands that depend on a large number of equally important variables are considered and conditions that make expedient quasi-Monte Carlo integrations are investigated for dimensions n≤300.

Global sensitivity indices for rather complex mathematical models can be efficiently computed by Monte Carlo (or quasi-Monte Carlo) methods. These indices are used for estimating the influence of individual variables or groups of variables on the model output.

Currently, in the context of quasi-Monte Carlo applications, the most effective low-discrepancy point sets and sequences are digital (t, m, s)-nets and (t, s)-sequences. In this survey we will consider ideas for the investigation of a new quality parameter reflecting projections of digital nets...

A model function f(x1,…,xn) defined in the unit hypercube Hn with Lebesque measure dx=dx1…dxn is considered. If the function is square integrable, global sensitivity indices provide adequate estimates for the influence of individual factors xi or groups of such factors. Alternative...