通胀风险下的鲁棒最优投资组合与再保险问题研究（英文）  

Robust Optimal Portfolio and Reinsurance for an Insurer under Inflation Risk

作　　者：欧辉[1] 黄娅[2] 杨向群[1] 周杰明[1] 

机构地区：[1]湖南师范大学数学与计算机科学学院,高性能计算与随机信息处理省部共建教育部重点实验室,长沙410081 [2]湖南大学工商管理学院,长沙410082

出　　处：《应用概率统计》2016年第1期89-100,共12页Chinese Journal of Applied Probability and Statistics

基　　金：supported by the National Natural Science Foundation of China(11171101,11571189);the Construct Program of the Key Discipline in Hunan Province

摘　　要：本文研究了一个保险公司带通胀风险的鲁棒最优投资组合与再保险问题,其中保险公司对模型不确定性是含糊厌恶的.我们假设保险公司不仅可以购买比例再保险,还可以在风险资产和无风险资产中进行投资.在模型不确定性框架中,本文的优化目标是使得保险公司的终端财富最小的情况下其幂效用达到最大.根据随机控制理论,获得了最优策略和值函数的显示表达式.In this paper, we investigate a robust optimal portfolio and reinsurance problem under inflation risk for an ambiguity-averse insurer （AAI）, who worries about uncertainty in model parameters. We assume that the AAI is allowed to purchase proportional reinsurance and invest his/her wealth in a financial market which consists of a risk-free asset and a risky asset. The objective of the AAI is to maximize the minimal expected power utility of terminal wealth. By using techniques of stochastic control theory, closed-form expressions for the value function and optimal strategies are obtained.

关 键 词：鲁棒控制 幂效用 投资组合 再保险 通胀 

分 类 号：O211.63[理学—概率论与数理统计] F224.11[理学—数学]