Reducing Bias in Event Time Simulations via Measure Changes

Stochastic point process models of event timing are common in many areas, including finance, insurance and reliability. Monte Carlo simula- tion 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 (exponential) martingales inducing changes of measure. Numerical results illustrate our approach