状态相依效用下的超额损失再保险--投资策略

doi:10.15960/j.cnki.issn.1007-6093.2016.01.009

运筹学学报

状态相依效用下的超额损失再保险--投资策略

谷爱玲¹ 陈树敏^2,*

1. 广东工业大学应用数学学院，广州 510006; 2. 广东工业大学管理学院，广州 510006;

收稿日期:2015-09-24 出版日期:2016-03-15 发布日期:2016-03-15
通讯作者: 陈树敏 chenshumin1@gmail.com
基金资助:
国家自然科学基金(Nos. 71501050, 71301031), 广东省自然科学基金(No. 2014A030310195), 广东工业大学校内博士启动基金

Optimal excess-of-loss reinsurance and investment strategy under state-dependent utility function

GU Ailing¹CHEN Shumin^2,*

1. School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510006, China; 2. School of Management, Guangdong University of Technology, Guangzhou 510006, China

Received:2015-09-24 Online:2016-03-15 Published:2016-03-15

摘要/Abstract

摘要：

假设保险公司的盈余过程和金融市场的资产价格过程均由可观测的连续时间马尔科夫链所调节, 以最大化终端财富的状态相依的期望指数效用为目标, 研究了保险公司的超额损失再保险-投资问题. 运用动态规划方法, 得到最优再保险-投资策略的解析解以及最优值函数的半解析式. 最后, 通过数值例子, 分析了模型各参数对最优值函数和最优策略的影响.

关键词: 机制转移, 超额损失再保险, 状态相依效用函数, Hamilton-Jacobi-Bellman方程

Abstract:

This paper studies an optimal excess-of-loss reinsurance and investment problem for an insurer, and aims to maximize the expected exponential utility from her terminal wealth with a state-dependent utility function. It is assumed that the surplus of the insurer and the financial market are modulated by an observable continuous-time Markov chain. By applying stochastic control theory, the explicit expression of optimal reinsurance-investment strategy is obtained. Finally, the impact of some parameters on the optimal strategy and optimal value function is given.

Key words: regime-switching, excess-of-loss reinsurance, state-dependent utility function, Hamilton-Jacobi-Bellman equation

谷爱玲, 陈树敏. 状态相依效用下的超额损失再保险--投资策略[J]. 运筹学学报, doi: 10.15960/j.cnki.issn.1007-6093.2016.01.009.

GU Ailing, CHEN Shumin. Optimal excess-of-loss reinsurance and investment strategy under state-dependent utility function[J]. Operations Research Transactions, doi: 10.15960/j.cnki.issn.1007-6093.2016.01.009.

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状态相依效用下的超额损失再保险--投资策略

Optimal excess-of-loss reinsurance and investment strategy under state-dependent utility function

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