扩散风险模型中随机时间区间最优分红和再保险问题

数学物理学报 ›› 2021, Vol. 41 ›› Issue (2): 538-547.

扩散风险模型中随机时间区间最优分红和再保险问题

刘晓(),姚鹏(),陈振龙*()

¹ 安徽师范大学数学与统计学院安徽芜湖 241003
² 浙江工商大学统计与数学学院杭州 310018

收稿日期:2020-04-27 出版日期:2021-04-26 发布日期:2021-04-29
通讯作者: 陈振龙 E-mail:yjjatyjjat@163.com;2845897419@qq.com;zlchenv@163.com
作者简介:刘晓, E-mail: yjjatyjjat@163.com|姚鹏, E-mail: 2845897419@qq.com
基金资助:
国家自然科学基金(11971432);安徽省自然科学基金(1908085MA21);安徽师范大学博士启动基金(2016XJJ119);教育部人文社会科学研究规划基金项目(18YJA910001);浙江省自然科学基金项目(LY21G010003)

On Optimal Dividend and Reinsurance Problems in the Diffusion Risk Model with Random Time Horizon

Xiao Liu(),Peng Yao(),Zhenlong Chen*()

¹ School of Mathematics and Statistics, Anhui Normal University, Anhui Wuhu 241003
² School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018

Received:2020-04-27 Online:2021-04-26 Published:2021-04-29
Contact: Zhenlong Chen E-mail:yjjatyjjat@163.com;2845897419@qq.com;zlchenv@163.com
Supported by:
the NSFC(11971432);the NSF of Anhui Province(1908085MA21);the Doctor Startup Funds of Anhui Normal University(2016XJJ119);the Humanities and Social Sciences Research Project of Ministry of Education(18YJA910001);the NSF of Zhejiang Province(LY21G010003)

摘要/Abstract

摘要：

该文在扩散风险模型中研究随机时间区间最优分红和再保险问题.假设应用比例再保险策略，随机时间服从指数分布，若破产时刻先于随机时刻到来，则在破产时刻存在一个固定数额的非负价值；若随机时刻先于破产时刻到来，则在随机时刻存在另一个固定数额的非负价值，得到了最优分红和再保险策略，以及值函数的表达式，并给出一个数值例子.

关键词: 最优分红, 最优再保险, 随机控制

Abstract:

This paper studies the optimal dividend and reinsurance problems in the diffusion risk model with random time horizon. Assume that the proportional reinsurance strategy is applied, the random time is exponentially distributed, and if the random time comes before ruin, a fixed nonnegative value exists, otherwise another fixed nonnegative value exists, the optimal dividend and reinsurance strategies and the explicit expressions of the value function are obtained, and a numerical example is presented.

Key words: Optimal dividends, Optimal reinsurance, Stochastic control

中图分类号:

O212.62

刘晓,姚鹏,陈振龙. 扩散风险模型中随机时间区间最优分红和再保险问题[J]. 数学物理学报, 2021, 41(2): 538-547.

Xiao Liu,Peng Yao,Zhenlong Chen. On Optimal Dividend and Reinsurance Problems in the Diffusion Risk Model with Random Time Horizon[J]. Acta mathematica scientia,Series A, 2021, 41(2): 538-547.

参考文献 19

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