Some new infinite series expansions for the first passage time densities in a jump diffusion model with phase-type jumps
作者：
Highlights：
• We propose a general theoretical framework for systematically deriving explicit closed-form expressions of the first passage time density functions in a class of jump diffusion processes with phase-type jumps.
• Our method is based on the projection idea in L2 space and theory of the Laguerre series.
• Two methods for deriving the Laguerre coefficients are proposed.
• A lot of numerical examples are given to show the effectiveness of the proposed method.
摘要
•We propose a general theoretical framework for systematically deriving explicit closed-form expressions of the first passage time density functions in a class of jump diffusion processes with phase-type jumps.•Our method is based on the projection idea in L2 space and theory of the Laguerre series.•Two methods for deriving the Laguerre coefficients are proposed.•A lot of numerical examples are given to show the effectiveness of the proposed method.
论文关键词：Jump diffusion model,Laguerre series,First passage time,Phase-type jumps
论文评审过程：Received 30 September 2021, Revised 10 May 2022, Accepted 13 May 2022, Available online 17 May 2022, Version of Record 17 May 2022.
论文官网地址：https://doi.org/10.1016/j.amc.2022.127251
