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

Jiayi Xie, Zhenyu Cui, Zhimin Zhang

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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.

Original languageEnglish
Article number127251
JournalApplied Mathematics and Computation
Volume429
DOIs
StatePublished - 15 Sep 2022

Keywords

  • First passage time
  • Jump diffusion model
  • Laguerre series
  • Phase-type jumps

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