Open AccessFirst passage problems of refracted jump diffusion processes and their applications in valuing equity-linked death benefits
Author(s) -
Meiqiao Ai,
Zhimin Zhang,
Wenguang Yu
Publication year - 2022
Publication title -
journal of industrial and management optimization
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.325
H-Index - 32
eISSN - 1553-166X
pISSN - 1547-5816
DOI - 10.3934/jimo.2021039
Subject(s) - laplace transform , jump , jump diffusion , lévy process , exponential function , equity (law) , first hitting time model , mathematics , ordinary differential equation , closed form expression , mathematical economics , mathematical analysis , differential equation , statistics , law , physics , quantum mechanics , political science
This paper studies some first passage time problems in a refracted jump diffusion process with hyper-exponential jumps. Closed-form expressions for four functions associated with the first passage time are obtained by solving some ordinary integro-differential equations. In addition, the obtained results are used to value equity-linked death benefit products with state-dependent fees. Specifically, we obtain the closed-form Laplace transform of the fair value of barrier option, which is further recovered by the bilateral Abate-Whitt algorithm. Numerical results confirm that the proposed approach is efficient.