Reducing Bias in Event Time Simulations via Measure Changes

Abstract

Stochastic point process models of event timing are common in many areas, including finance, insurance, and reliability. Monte Carlo simulation is often used to perform computations for these models. The standard sampling algorithm, which is based on a time-change argument, is widely applicable but generates biased simulation estimators. This article develops and analyzes a change of probability measure that can reduce or even eliminate the bias without restricting the scope of the algorithm. A result of independent interest offers new conditions that guarantee the existence of a broad class of point process martingales inducing changes of measure. Numerical results illustrate our approach.