考虑通胀风险与最低绩效保障的损失厌恶型保险公司的最优投资与再保险策略

数学物理学报 ›› 2022, Vol. 42 ›› Issue (4): 1265-1280.

• 论文 • 上一篇

考虑通胀风险与最低绩效保障的损失厌恶型保险公司的最优投资与再保险策略

季锟鹏(),彭幸春*()

武汉理工大学理学院武汉 430070

收稿日期:2021-07-26 出版日期:2022-08-26 发布日期:2022-08-08
通讯作者: 彭幸春 E-mail:jkp950801@163.com;pxch@whut.edu.cn
作者简介:季锟鹏, E-mail: jkp950801@163.com
基金资助:
国家自然科学基金青年项目(11701436);中央高校科研业务费专项资金(3120621545)

Optimal Investment and Reinsurance Strategies for Loss-averse Insurer Considering Inflation Risk and Minimum Performance Guarantee

Kunpeng Ji(),Xingchun Peng*()

School of Science, Wuhan University of Technology, Wuhan 430070

Received:2021-07-26 Online:2022-08-26 Published:2022-08-08
Contact: Xingchun Peng E-mail:jkp950801@163.com;pxch@whut.edu.cn
Supported by:
the NSFC(11701436);the Fundamental Research Funds for the Central Universities(3120621545)

摘要/Abstract

摘要：

该文研究了损失厌恶型保险公司的最优投资与再保险策略, 其中考虑了通胀风险与最低绩效保障. 假设保险盈余与通胀指数债券过程和股价过程具有相关性, 保险公司的投资选择包括通胀指数债券, 股票和无风险资产, 同时, 保险公司可以购买比例再保险来分散风险. 该文在期望S 型效用最大化准则下, 运用鞅方法得到了最优投资与再保险策略的详细表达式, 并通过数值模拟分析了参数变化对投资与再保险策略的影响.

关键词: 比例再保险, S 型效用, 通货膨胀, 最低绩效保障, 鞅方法

Abstract:

This paper studies the optimal investment and reinsurance strategies of a loss-averse insurer, considering inflation risk and minimum performance guarantee. Assume that the insurance surplus is correlated with the inflation-indexed bond process and the stock price process. The investment options of the insurer include inflation-indexed bond, stock and risk-free asset. Meanwhile, the insurer can purchase proportional reinsurance to diversify risks. Under the criterion of maximizing the expected S-shaped utility, the detailed expressions of the optimal investment and reinsurance strategies are derived by using the martingale method, and the influences of parameter variations on the investment and reinsurance strategies are analyzed by numerical simulations.

Key words: Proportional reinsurance, S-shaped utility function, Inflation, Minimum performance guarantee, Martingale method

中图分类号:

O211.6

季锟鹏,彭幸春. 考虑通胀风险与最低绩效保障的损失厌恶型保险公司的最优投资与再保险策略[J]. 数学物理学报, 2022, 42(4): 1265-1280.

Kunpeng Ji,Xingchun Peng. Optimal Investment and Reinsurance Strategies for Loss-averse Insurer Considering Inflation Risk and Minimum Performance Guarantee[J]. Acta mathematica scientia,Series A, 2022, 42(4): 1265-1280.

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[2]	黄玲,刘海燕,陈密. 基于Ornstein-Uhlenbeck过程下具有两个再保险公司的比例再保险与投资[J]. 数学物理学报, 2023, 43(3): 957-969.
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[4]	张昕丽, 孙文瑜. 考虑交易费用和债务的再保险和投资问题[J]. 数学物理学报, 2012, 32(1): 137-147.

考虑通胀风险与最低绩效保障的损失厌恶型保险公司的最优投资与再保险策略

Optimal Investment and Reinsurance Strategies for Loss-averse Insurer Considering Inflation Risk and Minimum Performance Guarantee

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