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 / √N, where N is the sample size, is achieved, which is in sharp contrast to the slower nonparametric rates achieved by kernel smoothing of cumulative distribution functions.
Citation
Tomoyuki Ichiba. Constantinos Kardaras. "Efficient estimation of one-dimensional diffusion first passage time densities via Monte Carlo simulation." J. Appl. Probab. 48 (3) 699 - 712, September 2011. https://doi.org/10.1239/jap/1316796908
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