OPTIMAL PROPORTIONAL REINSURANCE AND INVESTMENT FOR A CONSTANT ELASTICITY OF VARIANCE MODEL UNDER VARIANCE PRINCIPLE  

作　　者：周杰明 邓迎春 黄娅 杨向群 

机构地区：[1]School of Mathematical Sciences,Nankai University [2]College of Mathematics and Computer Science,Key Laboratory of High Performance Computing and Stochastic Information Processing Ministry of Education of China,Hunan Normal University [3]College of Business Administration,Hunan University

出　　处：《Acta Mathematica Scientia》2015年第2期303-312,共10页数学物理学报（B辑英文版）

基　　金：supported by the NSFC(11171101)

摘　　要：This article studies the optimal proportional reinsurance and investment problem under a constant elasticity of variance （CEV） model. Assume that the insurer＇s surplus process follows a jump-diffusion process, the insurer can purchase proportional reinsurance from the reinsurer via the variance principle and invest in a risk-free asset and a risky asset whose price is modeled by a CEV model. The diffusion term can explain the uncertainty associated with the surplus of the insurer or the additional small claims. The objective of the insurer is to maximize the expected exponential utility of terminal wealth. This optimization problem is studied in two cases depending on the diffusion term＇s explanation. In all cases, by using techniques of stochastic control theory, closed-form expressions for the value functions and optimal strategies are obtained.This article studies the optimal proportional reinsurance and investment problem under a constant elasticity of variance （CEV） model. Assume that the insurer＇s surplus process follows a jump-diffusion process, the insurer can purchase proportional reinsurance from the reinsurer via the variance principle and invest in a risk-free asset and a risky asset whose price is modeled by a CEV model. The diffusion term can explain the uncertainty associated with the surplus of the insurer or the additional small claims. The objective of the insurer is to maximize the expected exponential utility of terminal wealth. This optimization problem is studied in two cases depending on the diffusion term＇s explanation. In all cases, by using techniques of stochastic control theory, closed-form expressions for the value functions and optimal strategies are obtained.

关 键 词：Constant elasticity of variance Hami!ton-Jacobi-Bellman equation jump-diffusion process exponential utility REINSURANCE 

分 类 号：O212.1[理学—概率论与数理统计] F842.3[理学—数学]