指数均值回复金融市场下的最优投资和最优再保险策略  

Optimal Reinsurance and Investment Policies under Exponential Mean-Reversion Financial Market

作　　者：李启才[1] 顾孟迪[2] 

机构地区：[1]南京师范大学数学科学学院,江苏南京210023 [2]上海交通大学安泰经济与管理学院,上海200052

出　　处：《管理工程学报》2016年第4期79-84,共6页Journal of Industrial Engineering and Engineering Management

基　　金：国家自然科学基金资助项目(61304065;11471165);南京师范大学青蓝工程项目

摘　　要：近来,随机控制理论广泛应用于精算数学领域。这是因为保险公司的资产管理越来越技术化。保险公司可以通过购买再保险来控制和转移它们的风险,通过投资金融市场来管理它们的利润。为了更好的利用这些机会,它们需要随机控制的技巧。本文利用带有漂移的布朗运动描述索赔过程,在终端指数效用最大化的目标下,考虑保险公司的最优再保险和投资决策。文章假定保险公司投资于指数均值回复的金融市场。同时保险公司通过购买一个纯比例或者纯超额损失亦或是二者组合的再保险来转移索赔风险。利用随机控制理论,获得了值函数、最优再保险和投资策略的表达式。最优投资策略中第一项类似经典Merton策略:投资风险资产资金与单位风险溢价成正比。第二和第三项则分别是根据资产价格和时间对投资行为的调整。文章也证明了最优的再保险策略是购买一个纯的超额损失再保险,而非纯比例或组合再保险,从而也说明超额损失再保险总是优于比例再保险。最后给出了一些数值例子。There has been an increasing interest in the use of stochastic optimal control theory in actuarial mathematics. This is due to the fact nowadays the asset-liability management of insurance companies is becoming more and more technical and increasing intertwined with the financial sector. Major insurance companies have opportunity to invest part of their reserves into financial market and take reinsurance to manage and control their exposure to risk. In order to make the best use of these opportunities, they need the techniques of optimal control. In this paper, claim risk process was modeled by Brownian motion with drift, and the optimization problem was studied of maximizing the exponential utility of terminal wealth under the controls of combining quota-share and excess-of-loss reinsurance and investment, we consider the insurer invests its wealth in exponential mean-reversion stock market. And, the insurer has a choice of reinsuring his claim risk either by a pure quota-share treaty, or by a pure excess of loss treaty or by any combination of the two. Using stochastic control theory, explicit expressions for the optimal polices and value function are obtained. The first term of optimal investment strategy is analogous to the classical Merton investment policy, which says that it is optimal to invest a fraction in the risky asset proportional to the risk premium per unit risk. The second and the third term of investment strategy adjust the investment behavior according to price level of asset and time respectively. We also show that the optimal excess-of-loss reinsurance is always better than combining quota-share and excess -of-loss reinsurance. And some numerical examples are given.

关 键 词：随机控制 再保险 指数均值回复 效用函数 

分 类 号：F830.91[经济管理—金融学]