OPTIMAL IMPORTANCE SAMPLING PARAMETER SEARCH FOR L′EVY PROCESSES VIA STOCHASTIC APPROXIMATION

摘要

The author proposes stochastic approximation methods of finding the optimal measure change by the exponential tilting for L′evy processes in Monte Carlo importance sampling variance reduction. In accordance with the structure of the underlying L′evy measure, either a constrained or unconstrained algorithm of the stochastic approximation is chosen. For both cases, the almost sure convergence to a unique stationary point is proved. Numerical examples are presented to illustrate the effectiveness of our method.