Subsolutions of an Isaacs Equation and Efficient Schemes for Importance Sampling: Examples and Numerics

Abstract

Abstract : It has been established that importance sampling algorithms for estimating rare-event probabilities are intimately connected with two-person zero-sum differential games and the associated Isaacs equation. The purpose of the present paper and a companion paper is to show that the classical sense subsolutions of the Isaacs equation can be used as a basic and flexible tool for the construction and analysis of efficient importance sampling schemes. The importance sampling algorithms based on subsolutions are dynamic in the sense that during the course of a single simulation, the change of measure used at each time step may depend on the outcome of the simulation up until that time. While focused on theoretical aspects, the present paper discusses explicit methods of constructing subsolutions, implementation issues, and simulation results.