Efficient Estimation of One-Dimensional Diffusion First Passage Time Densities via Monte Carlo Simulation release_r6a4ttubgvgljh2tiybatzkot4

Abstract

We propose a method for estimating first passage time densities of one-dimensional diffusions via Monte Carlo simulation. Our approach involves a representation of the first passage time density as the expectation of a functional of the three-dimensional Brownian bridge. As the latter process can be simulated exactly, our method leads to almost unbiased estimators. Furthermore, since the density is estimated directly, a convergence of order 1 / √<jats:italic>N</jats:italic>, where <jats:italic>N</jats:italic> is the sample size, is achieved, which is in sharp contrast to the slower nonparametric rates achieved by kernel smoothing of cumulative distribution functions.
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