带通货膨胀风险的最优再保险和投资策略  

Optimal Reinsurance and Investment Strategy with Inflation Risks

作　　者：魏宽飞 王文胜[1] WEI Kuanfei;WANG Wensheng(School of Science,Hangzhou Normal University,Hangzhou 310036,China)

机构地区：[1]杭州师范大学理学院,浙江杭州310036

出　　处：《杭州师范大学学报（自然科学版）》2018年第4期411-417,共7页Journal of Hangzhou Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11671115);浙江省自然科学基金项目(LY14A010025)

摘　　要：用带漂移的布朗运动去逼近保险公司的盈余过程,假设有两家再保险公司承担保险公司的风险,采用混合比例再保险策略.另一方面,将保险公司把资产盈余全部投资到风险资产和无风险资产,同时考虑通货膨胀风险,将风险资产在通货膨胀风险下进行折算.运用动态规划原理,研究了保险公司的终端财富期望效用最大化,得出最优混合比例再保险和投资策略显示解,并分析了最优再保险和最优投资策略的灵敏度.Using a drifted Brownian motion to closely approach the surplus process of an insurance company,the paper assumes that two reinsurance companies take the risk instead of insurance companies through the strategy of mixed proportion reinsurance.On the other hand,the insurance companies invest all surplus assets into risky assets and risk-free assets,taking the risk of inflation into account at the same time,and convert risky assets under the risk of inflation.It uses the dynamic programming theory to study the utility maximization of terminal wealth,gets the strategy with optimal mixed ratio of reinsurance and investment,and analyzes the sensitivity of optimal reinsurance and optimal investment strategy as well.

关 键 词：混合比例再保险 通货膨胀 期望效用 Hamilton-Jacob-Bellman方程 方差保费准则 

分 类 号：O211.9[理学—概率论与数理统计] O224[理学—数学]