TY - JOUR
T1 - Some new infinite series expansions for the first passage time densities in a jump diffusion model with phase-type jumps
AU - Xie, Jiayi
AU - Cui, Zhenyu
AU - Zhang, Zhimin
N1 - Publisher Copyright:
© 2022
PY - 2022/9/15
Y1 - 2022/9/15
N2 - 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.
AB - 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.
KW - First passage time
KW - Jump diffusion model
KW - Laguerre series
KW - Phase-type jumps
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U2 - 10.1016/j.amc.2022.127251
DO - 10.1016/j.amc.2022.127251
M3 - Article
AN - SCOPUS:85130169169
SN - 0096-3003
VL - 429
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
M1 - 127251
ER -