考虑通胀风险与最低绩效保障的损失厌恶型保险公司的最优投资与再保险策略  

Optimal Investment and Reinsurance Strategies for Loss-averse Insurer Considering Inflation Risk and Minimum Performance Guarantee

作　　者：季锟鹏 彭幸春 Ji Kunpeng;Peng Xingchun(School of Science,Wuhan University of Technology,Wuhan 430070)

机构地区：[1]武汉理工大学理学院,武汉430070

出　　处：《数学物理学报（A辑）》2022年第4期1265-1280,共16页Acta Mathematica Scientia

基　　金：国家自然科学基金青年项目(11701436);中央高校科研业务费专项资金(3120621545)。

摘　　要：该文研究了损失厌恶型保险公司的最优投资与再保险策略,其中考虑了通胀风险与最低绩效保障.假设保险盈余与通胀指数债券过程和股价过程具有相关性,保险公司的投资选择包括通胀指数债券,股票和无风险资产,同时,保险公司可以购买比例再保险来分散风险.该文在期望S型效用最大化准则下,运用鞅方法得到了最优投资与再保险策略的详细表达式,并通过数值模拟分析了参数变化对投资与再保险策略的影响.This paper studies the optimal investment and reinsurance strategies of a lossaverse insurer,considering inflation risk and minimum performance guarantee.Assume that the insurance surplus is correlated with the inflation-indexed bond process and the stock price process.The investment options of the insurer include inflation-indexed bond,stock and riskfree asset.Meanwhile,the insurer can purchase proportional reinsurance to diversify risks.Under the criterion of maximizing the expected S-shaped utility,the detailed expressions of the optimal investment and reinsurance strategies are derived by using the martingale method,and the influences of parameter variations on the investment and reinsurance strategies are analyzed by numerical simulations.

关 键 词：比例再保险 S型效用 通货膨胀 最低绩效保障 鞅方法 

分 类 号：O211.6[理学—概率论与数理统计]