Exact simulation of diffusion first exit times: algorithm acceleration

TL;DR

This paper introduces an accelerated algorithm for the exact simulation of diffusion process exit times, leveraging a multi-armed bandit model to improve computational efficiency, with demonstrated numerical benefits.

Contribution

It develops an acceleration method for the GDET-algorithm using multi-armed bandit techniques, enhancing the practicality of exact diffusion exit time simulations.

Findings

Significant reduction in simulation time demonstrated

Effective application of bandit model for algorithm acceleration

Numerical examples confirm improved efficiency

Abstract

In order to describe or estimate different quantities related to a specific random variable, it is of prime interest to numerically generate such a variate. In specific situations, the exact generation of random variables might be either momentarily unavailable or too expensive in terms of computation time. It therefore needs to be replaced by an approximation procedure. As was previously the case, the ambitious exact simulation of exit times for diffusion processes was unreachable though it concerns many applications in different fields like mathematical finance, neuroscience or reliability. The usual way to describe exit times was to use discretization schemes, that are of course approximation procedures. Recently, Herrmann and Zucca \cite{Herrmann-Zucca-2} proposed a new algorithm, the so-called GDET-algorithm (General Diffusion Exit Time), which permits to simulate exactly the exit time for one-dimensional diffusions. The only drawback of exact simulation methods using an acceptance-rejection sampling is their time consumption. In this paper the authors highlight an acceleration procedure for the GDET-algorithm based on a multi-armed bandit model. The efficiency of this acceleration is pointed out through numerical examples.