Journal of Applied Probability

Efficient estimation of one-dimensional diffusion first passage time densities via Monte Carlo simulation

Tomoyuki Ichiba and Constantinos Kardaras

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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.

Article information

Source
J. Appl. Probab. Volume 48, Number 3 (2011), 699-712.

Dates
First available in Project Euclid: 23 September 2011

Permanent link to this document
https://projecteuclid.org/euclid.jap/1316796908

Digital Object Identifier
doi:10.1239/jap/1316796908

Mathematical Reviews number (MathSciNet)
MR2884809

Zentralblatt MATH identifier
1230.65003

Subjects
Primary: 65C05: Monte Carlo methods 60G44: Martingales with continuous parameter

Keywords
First passage time Monte Carlo density estimation one-dimensional diffusion three-dimensional Brownian bridge rate function

Citation

Ichiba, Tomoyuki; Kardaras, Constantinos. Efficient estimation of one-dimensional diffusion first passage time densities via Monte Carlo simulation. J. Appl. Probab. 48 (2011), no. 3, 699--712. doi:10.1239/jap/1316796908. https://projecteuclid.org/euclid.jap/1316796908


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