保险公司最优比例再保险和配对交易策略

Optimal Proportional Reinsurance and Pairs Trading Polices for Insurer

考虑保险公司通过比例再保险转移索赔风险和配对交易策略管理财富的优化问题.利用经典的复合泊松索赔过程描述保险公司的盈余,同时保险公司投资包含一份股票多头和若干份股票空头的配对资产组合,该资产价差服从均值-回复过程.在终端财富期望指数效用最大化的准则下,利用随机控制理论获得最优的比例再保险和投资策略及值函数的解析式.

This paper discusses optimization problem which the insurer transfer the claims risk by proportional reinsurance and manage the wealth by pairs trading. The surplus of claims is modeled by compound Poisson process. And the insurer can invest it’s wealth into pairs portfolio which include a long position on one stock and a short on another stock. The price spread of this pair follows a mean-reverting stochastic process. Under maximizing of expect exponent utility of the terminal wealth,the optimal proportional reinsurance and pairs trading polices and value function are solved by stochastic control theory.