FIRST PASSAGE PROBLEMS OF REFRACTED JUMP DIFFUSION PROCESSES AND THEIR APPLICATIONS IN VALUING EQUITY-LINKED DEATH BENEFITS

被引：2

作者：

Ai, Meiqiao ^{[1
]}

Zhang, Zhimin ^{[1
]}

Yu, Wenguang ^{[2
]}

机构：

[1] Chongqing Univ, Coll Math & Stat, Chongqing 401331, Peoples R China

[2] Shandong Univ Finance & Econ, Sch Insurance, Jinan 250014, Peoples R China

来源：

JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION | 2022年 / 18卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Refracted jump diffusion processes; First passage time; Equity-linked death benefits; Laplace trans-form; OCCUPATION TIMES; LEVY; OPTIONS; FEES;

D O I：

10.3934/jimo.2021039

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

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 al-gorithm. Numerical results confirm that the proposed approach is efficient.

引用

下载

页码：1689 / 1707

页数：19

共 38 条

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[32] TheW,Zscale functions kit for first passage problems of spectrally negative Levy processes, and applications to control problems
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[33] Iterative algorithm for the first passage time distribution in a jump-diffusion model with regime-switching, and its applications
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[34] Residual mean first-passage time for jump processes: theory and applications to Levy flights and fractional Brownian motion
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Benichou, O.
Metzler, Ralf
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[35] More general problems on first-passage times for diffusion processes: A new version of the fptdApprox R package
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Serrano-Perez, J. J.
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[37] The First Passage Time Problem for Gauss-Diffusion Processes: Algorithmic Approaches and Applications to LIF Neuronal Model
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[38] A radial basis function approach to compute the first-passage probability density function in two-dimensional jump-diffusion models for financial and other applications
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