Abstract

In this paper, we develop a Monte Carlo based algorithm for estimating the FPT (first passage time) density of the solution of a one-dimensional time-homogeneous SDE (stochastic differential equation) through a time-dependent frontier. We consider Brownian bridges as well as local 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.

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