Pricing of catastrophe bonds leads to integrals with discontinuous and formally infinite-dimensional integrands. We investigate the suitability of QuasiMonte Carlo methods for the numerical evaluation of these integrals and develop several variance-reduction algorithms. Furthermore, the performance of Quasi-Monte Carlo sequences for asymptotically efficient rare event simulation is examined. Va...

Statistical analysis tasks are increasingly encountered in the design of digital circuits that implement complex Boolean functions. Examples include analyzing the impact of soft errors, estimating power consumption, and stochastic computation. Common simulation techniques such as quasiMonte Carlo simulation often converge too slowly for large circuits with many inputs, i.e., many dimensions. We...

This paper presents an overview of techniques for improving the efficiency of option pricing simulations, including quasiMonte Carlo methods, variance reduction, and methods for dealing with discretization error.

This article is dedicated to the computation of the moments of the solution to stochastic partial differential equations with log-normal distributed diffusion coefficient by the Quasi-Monte Carlo method. Our main result is the polynomial tractability for the QuasiMonte Carlo method based on the Halton sequence. As a by-product, we obtain also the strong tractability of stochastic partial differ...

In the context of multi-factor stochastic volatility models, which contain the widely used Heston model, we present variance reduction techniques to price European options by Monte Carlo (MC) and QuasiMonte Carlo (QMC) methods. We formulate a stochastic integral as a martingale control for the payoffs to be evaluated. That control corresponds to the cost of an approximate delta hedging strategy...

We consider a mathematical model for polymeric liquids which requires the solution of high-dimensional Fokker-Planck equations related to stochastic differential equations. While Monte-Carlo (MC) methods are classically used to construct approximate solutions in this context, we consider an approach based on QuasiMonte-Carlo (QMC) approximations. Although QMC has proved to be superior to MC in ...

A general concept for parallelizing quasi-Monte Carlo methods is introduced. By considering the distribution of computing jobs across a multiprocessor as an additional problem dimension, the straightforward application of quasiMonte Carlo methods implies parallelization. The approach in fact partitions a single low-discrepancy sequence into multiple low-discrepancy sequences. This allows for ad...

In this paper we discuss the issue of solving stochastic optimization problems using sampling methods. Numerical results have shown that using variance reduction techniques from statistics can result in significant improvements over Monte Carlo sampling in terms of the number of samples needed for convergence of the optimal objective value and optimal solution to a stochastic optimization probl...

In the last decade considerable practical interest, e.g. in credit and insurance risk or telecommunication applications, as well as methodological challenges caused intensive research on estimation of rare event probabilities. This article aims to show that recently developed rare event estimators are especially well-suited for a quasiMonte Carlo framework by establishing limit relations for th...

In many spatial analysis contexts, the variable of interest is discrete and there is spatial clustering of observations. This paper formulates a model that accommodates clustering along more than one dimension in the context of a discrete response variable. For example, in a travel mode choice context, individuals are clustered by both the home zone in which they live as well as by their work l...