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

摘要

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