Some new infinite series expansions for the first passage time densities in a jump diffusion model with phase-type jumps

Jiayi Xie, Zhenyu Cui and Zhimin Zhang

Applied Mathematics and Computation, 2022, vol. 429, issue C

Abstract: We propose for the first time some explicit closed-form Laguerre series expansion formulas for the first passage time density functions of a jump diffusion model. Suppose that the jumps in the model are phase-type distributed. In contrast to existing methods in the literature based on numerical Laplace transform inversion, the proposed formulas are in analytical closed-form and simple to implement. Two different methods are proposed to compute the Laguerre coefficients. Various numerical examples are also given to show the effectiveness of our method.

Keywords: Jump diffusion model; Laguerre series; First passage time; Phase-type jumps (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:429:y:2022:i:c:s0096300322003253

DOI: 10.1016/j.amc.2022.127251

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