SAHARA效用函数下的保险人的最优投资策略  

Optimal Investment Strategies for an Insurer with SAHARA Utility

作　　者：赵倩 朱绍辉 ZHAO Qian;ZHU Shaohui(School of Statistics and Information,Shanghai University of International Business and Economics,Shanghai,201620,China)

机构地区：[1]上海对外经贸大学统计与信息学院,上海201620

出　　处：《应用概率统计》2020年第2期181-196,共16页Chinese Journal of Applied Probability and Statistics

基　　金：The project was supported by the National Natural Science Foundation of China(Grant No.11601320).

摘　　要：在本文中,我们考虑带有SAHARA效用函数的保险人的最优投资策略,目标是最大化其终端财富效用.这类效用函数拥有非单调的绝对风险厌恶,比CARA和CRRA效用函数更加灵活.在风险过程和股票过程分别由布朗运动和几何布朗运动刻画的情形下,我们采用鞅方法分别得到了临界值为常数和临界值动态服从一个明确过程的情况下的显示解.最后,我们证明最优投资策略是状态独立的.In this paper,we consider the optimal investment strategy which maximizes the utility of the terminal wealth of an insurer with SAHARA utility functions.This class of utility functions has non-monotone absolute risk aversion,which is more flexible than the CARA and CRRA utility functions.In the case that the risk process is modeled as a Brownian motion and the stock process is modeled as a geometric Brownian motion,we get the closed-form solutions for our problem by the martingale method for both the constant threshold and when the threshold evolves dynamically according to a specific process.Finally,we show that the optimal strategy is state-dependent.

关 键 词：最优投资策略 SAHARA效用函数 保险人 鞅方法 

分 类 号：O29[理学—应用数学] O232[理学—数学]