Explicit asymptotic on first passage times of diffusion processes

Angelos Dassios and Luting Li

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: We introduce a unified framework for solving first passage times of time- homogeneous diffusion processes. According to the potential theory and the perturbation theory, we are able to deduce closed-form truncated probability densities, as asymptotics or approximations to the original first passage time densities, for the single-side level crossing problems. The framework is applicable to diffusion processes with continuous drift functions; especially, for bounded drift functions, we show that the perturbation series converges. In the present paper, we demonstrate examples of applying our framework to the Ornstein-Uhlenbeck, Bessel, exponential-Shiryaev (studied in [13]), and the hypergeometric diffusion [8] processes. The purpose of this paper is to provide a fast and accurate approach to estimate first passage time densities of various diffusion processes.

Keywords: First Passage Time; Diffusion Process; Perturbation theory; Ornstein-Uhlenbeck Process; Bessel process; Exponential-Shiryaev Process; Hypergeometric Diffusion; Special functions (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Pages: 34 pages
Date: 2020-07-15
New Economics Papers: this item is included in nep-ore
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Published in Advances in Applied Probability, 15, July, 2020, 52(2). ISSN: 0001-8678

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