Optimal Reinsurance and Investment Strategy with Delay in Heston’s SV Model

doi:10.1007/s40305-020-00331-8

Journal of the Operations Research Society of China ›› 2021, Vol. 9 ›› Issue (2): 245-271.doi: 10.1007/s40305-020-00331-8

收稿日期:2018-03-25 修回日期:2020-02-11 出版日期:2021-06-30 发布日期:2021-06-08

Optimal Reinsurance and Investment Strategy with Delay in Heston’s SV Model

Chun-Xiang A¹, Ai-Lin Gu², Yi Shao¹

1. School of Mathematics and Statistics, Zhaoqing University, Zhaoqing 526061, Guangdong, China;
2. School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, China

Received:2018-03-25 Revised:2020-02-11 Online:2021-06-30 Published:2021-06-08
Contact: Yi Shao, Chun-Xiang A, Ai-Lin Gu E-mail:mathsyishao@126.com;acxgmaria@hotmail.com;ailing727@sohu.com
Supported by:
This research was supported by the National Natural Science Foundation of China (No.71801186),the Science Foundation of Ministry of Education of China (No.18YJC630001),and the Natural Science Foundation of Guangdong Province of China (No.2017A030310660).

摘要/Abstract

Abstract: In this paper, we consider an optimal investment and proportional reinsurance problem with delay, in which the insurer’s surplus process is described by a jump-diffusion model. The insurer can buy proportional reinsurance to transfer part of the insurance claims risk. In addition to reinsurance, she also can invests her surplus in a financial market, which is consisted of a risk-free asset and a risky asset described by Heston’s stochastic volatility (SV) model. Considering the performance-related capital flow, the insurer’s wealth process is modeled by a stochastic differential delay equation. The insurer’s target is to find the optimal investment and proportional reinsurance strategy to maximize the expected exponential utility of combined terminal wealth. We explicitly derive the optimal strategy and the value function. Finally, we provide some numerical examples to illustrate our results.

Key words: Proportional reinsurance, Stochastic differential delay equation (SDDE), Heston’s stochastic volatility (SV) model, Hamilton–Jacobi–Bellman (HJB) equation

中图分类号:

. [J]. Journal of the Operations Research Society of China, 2021, 9(2): 245-271.

Chun-Xiang A, Ai-Lin Gu, Yi Shao. Optimal Reinsurance and Investment Strategy with Delay in Heston’s SV Model[J]. Journal of the Operations Research Society of China, 2021, 9(2): 245-271.

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Optimal Reinsurance and Investment Strategy with Delay in Heston’s SV Model

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