随机时间区间通过分红和再保险最大化保险公司价值

数学物理学报 ›› 2023, Vol. 43 ›› Issue (6): 1843-1854.

随机时间区间通过分红和再保险最大化保险公司价值

刘晓(),叶阳帅(),徐林^*()

安徽师范大学数学与统计学院安徽芜湖 241003

收稿日期:2021-11-16 修回日期:2022-10-18 出版日期:2023-12-26 发布日期:2023-11-16
通讯作者: *徐林，E-mail: ahnuxulin@163.com
作者简介:刘晓，E-mail: yjjatyjjat@163.com|叶阳帅，E-mail: ahnuyeyangshuai@163.com
基金资助:
国家自然科学基金(11971034);教育部人文社科基金(17YJC910009);安徽省自然科学基金(1908085MA21)

Maximizing Insurer's Firm Value by Dividend and Reinsurance with a Random Time Horizon

Liu Xiao(),Ye Yangshuai(),Xu Lin^*()

School of Mathematics and Statistics, Anhui Normal University, Anhui Wuhu 241003

Received:2021-11-16 Revised:2022-10-18 Online:2023-12-26 Published:2023-11-16
Supported by:
NSFC(11971034);Education of Humanities and Social Science Fund Project(17YJC910009);Natural Science Foundation of Anhui Province(1908085MA21)

摘要/Abstract

摘要：

该文研究了随机时间区间保险公司的最优分红和再保险策略. 保险人的目标是在随机时间或破产时间到达时使保险公司的价值最大化. 这个价值由三部分组成: 到随机时间或破产时间的分红, 随机时间或破产时间的盈余和公司的品牌价值. 该文使用随机控制方法确定保险公司的联合最优策略. 结果显示, 当且仅当品牌价值或盈余过高时, 管理者应考虑不进行再保险, 当盈余增加时购买更少的再保险, 而分红总是采用障碍策略进行分配.

关键词: 偿付能力监管, 分红, 再保险, 品牌价值, 随机控制

Abstract:

In this paper, we investigates optimal dividend and reinsurance policies for an insurer with a random time horizon. The goal of the insurer is to maximize the value of the insurance company when the random time or the ruin time arrives. This value consists of three parts: the dividends up to the random time or the ruin time, the surplus at the random time or the ruin time and the company's brand value. We identify the insurer's joint optimal strategies using stochastic control methods. The results reveal that managers should consider no reinsurance if and only if the brand value or the surplus is too high, less reinsurance is bought when the surplus increases, and dividends are always distributed using the barrier strategy.

Key words: Solvency regulation, Dividend, Reinsurance, Brand value, Stochastic control

中图分类号:

O212.62

刘晓, 叶阳帅, 徐林. 随机时间区间通过分红和再保险最大化保险公司价值[J]. 数学物理学报, 2023, 43(6): 1843-1854.

Liu Xiao, Ye Yangshuai, Xu Lin. Maximizing Insurer's Firm Value by Dividend and Reinsurance with a Random Time Horizon[J]. Acta mathematica scientia,Series A, 2023, 43(6): 1843-1854.

图/表 4

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