Estimation of first passage time densities of diffusions processess through time-varying boundaries

TL;DR

This paper introduces a Monte Carlo algorithm for estimating the first passage time density of diffusion processes through dynamic boundaries, using Brownian bridges and Daniels curve approximations for improved tractability.

Contribution

It presents a novel Monte Carlo method combining Brownian bridges and Daniels curve approximations for efficient FPT density estimation with time-varying boundaries.

Findings

Effective estimation of FPT densities for time-dependent boundaries

Utilization of Daniels curves simplifies complex boundary crossing problems

Algorithm applicable to various diffusion processes

Abstract

In this paper, we develop a Monte Carlo based algorithm for estimating the FPT density of a time-homogeneous SDE through a time-dependent frontier. We consider Brownian bridges as well as localized Daniels curve approximations to obtain tractable estimations of the FPT probability between successive points of a simulated path of the process. Under mild assumptions, a (unique) Daniels curve local approximation can easily be obtained by explicitly solving a non-linear system of equations.