Linear-quadratic optimal control for discrete-time stochastic descriptor systems
Filled function method to optimize supply chain transportation costs
First passage problems of refracted jump diffusion processes and their applications in valuing equity-linked death benefits
Meiqiao Ai 1, , Zhimin Zhang 1,, and Wenguang Yu 2,
College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China
School of Insurance, Shandong University of Finance and Economics, Jinan 250014, China
* Corresponding author: Zhimin Zhang
Received August 2020 Revised November 2020 Early access March 2021
Fund Project: Zhimin Zhang is supported by the National Natural Science Foundation of China [grant number 11871121], Natural Science Foundation Project of CQ CSTC [grant number cstc2019jcyj-msxmX0004] and the Fundamental Research Funds for the Central Universities (project number 2020CDJSK02ZH03). Wenguang Yu is supported by the National Social Science Foundation of China (No. 15BJY007), the Taishan Scholars Program of Shandong Province (No. tsqn20161041), the Humanities and Social Sciences Project of the Ministry Education of China (No. 19YJA910002), the Natural Science Foundation of Shandong Province (No. ZR2018MG002), the Fostering Project of Dominant Discipline and Talent Team of Shandong Province Higher Education Institutions (No. 1716009), Shandong Provincial Social Science Project Planning Research Project (No. 19CQXJ08), the Risk Management and Insurance Research Team of Shandong University of Finance and Economics, Excellent Talents Project of Shandong University of Finance and Economics, the Collaborative Innovation Center Project of the Transformation of New and old Kinetic Energy and Government Financial Allocation
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.
Keywords: Refracted jump diffusion processes, First passage time, Laplace transform, Equity-linked death benefits.
Citation: Meiqiao Ai, Zhimin Zhang, Wenguang Yu. First passage problems of refracted jump diffusion processes and their applications in valuing equity-linked death benefits. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2021039
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Table 1. Pricing up-and-in call options when $ K $ varies, $ B = 120 $ and $ L = 115 $.
$ \sigma = 0.1 $ $ \sigma = 0.2 $
$ \lambda $ $ K $ $ \mathcal{M}_{3} $ $ \mathcal{M}_{5} $ $ \mathcal{M}_{10} $ $ \mathcal{M}_{3} $ $ \mathcal{M}_{5} $ $ \mathcal{M}_{10} $
1 100 64.56585 64.55930 64.54628 68.75548 68.75253 68.74360
105 64.36554 64.35829 64.34406 68.60582 68.60241 68.59308
Table 2. Pricing up-and-in call options when $ L $ varies, $ B = 120 $ and $ K = 100 $.
$ \sigma=0.1 $ $ \sigma=0.2 $
$ \lambda $ $ L $ $ \mathcal{M}_{3} $ $ \mathcal{M}_{5} $ $ \mathcal{M}_{10} $ $ \mathcal{M}_{3} $ $ \mathcal{M}_{5} $ $ \mathcal{M}_{10} $
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Meiqiao Ai Zhimin Zhang Wenguang Yu