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

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  • Xie, Jiayi
  • Cui, Zhenyu
  • Zhang, Zhimin

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.

Suggested Citation

  • Xie, Jiayi & Cui, Zhenyu & Zhang, Zhimin, 2022. "Some new infinite series expansions for the first passage time densities in a jump diffusion model with phase-type jumps," Applied Mathematics and Computation, Elsevier, vol. 429(C).
    • Handle: RePEc:eee:apmaco:v:429:y:2022:i:c:s0096300322003253
    DOI: 10.1016/j.amc.2022.127251
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    References listed on IDEAS

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