均值方差准则下的投资与再保险对比研究

Comparative Study of Investment and Reinsurance under the Mean-Variance Criterion

摘要: 本文旨在研究保险公司在终端时间确定情形下的最优适应性和确定性投资与再保险问题，首先假定保险公司的盈余可以投资于一个无风险资产和一个风险资产，再保险的形式为比例再保险，然后分析风险资产投资与再保险的综合财富过程，通过建立适当的均值–方差模型，运用如HJB方程等方法，求解对应问题中的最优投资和再保险策略的解析表达式，对比分析该情形下发现确定性策略结果皆优于适应性策略。最后分析获得的最优策略与经济参数的关系，得出一般结论：当风险资产的预期回报率或其波动率减小时，最优投资比例增大；当保险盈余的收益率或其波动率减小时，最优再保险比例增大；当再保费率相对保费的安全负载增大或再保费安全负载增大时，最优再保险比例也会增大。

Abstract: The aim of this paper is to study the optimal deterministic and adaptive investment and reinsurance of insurance companies in the case of deterministic terminal time. First, we assume that insurance company can invest in a risk-free asset and a risky asset, re the form of a proportional reinsurance, then analyze process of comprehensive wealth with risk assets investment and reinsurance, through the establishment of appropriate mean-variance model, and use methods such as HJB equation, the analytical expressions of the optimal investment and reinsurance strategies in the corresponding problems are solved, and the results of the deterministic strategies are found to be superior to the adaptive strategies under the comparative analysis of this situation. The uncertainty of investment termination time is further discussed. The general conclusion is drawn: the expected rate of return of a risky asset increases or its volatility decreases, the optimal investment proportion increases; the yield of insurance surplus increases or its volatility decreases, the optimal reinsurance ratio increases; the reinsurance rate relative to the safe load of the premium or the safe load of the premium increases, the optimal reinsurance ratio will also increase.