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

doi:10.1016/S0252-9602(15)60002-9

Acta mathematica scientia,Series B ›› 2015, Vol. 35 ›› Issue (2): 303-312.doi: 10.1016/S0252-9602(15)60002-9

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

Jieming ZHOU¹, Yingchun DENG², Ya HUANG³, Xiangqun YANG⁴

1. School of Mathematical Sciences, Nankai University, Tianjin 300071, China;
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, Changsha 410081, China;
3. College of Business Administration, Hunan University, Changsha 410082, China;
4. College of Mathematics and Computer Science, Key Laboratory of High Performance Computing and Stochastic Information Processing Ministry of Education of China, Hunan Normal University, Changsha 410081, China

Received:2012-09-12 Revised:2014-03-31 Online:2015-03-20 Published:2015-03-20
Contact: Jieming ZHOU School of Mathematical Sciences, Nankai University, Tianjin 300071, China E-mail: zhjm04101@126.com E-mail:zhjm04101@126.com
Supported by:
This work is supported by the NSFC (11171101).

Abstract

Abstract:

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.

Key words: Constant elasticity of variance, Hamilton-Jacobi-Bellman equation, jump-diffusion process, exponential utility, reinsurance

CLC Number:

62P05

Jieming ZHOU, Yingchun DENG, Ya HUANG, Xiangqun YANG. OPTIMAL PROPORTIONAL REINSURANCE AND INVESTMENT FOR A CONSTANT ELASTICITY OF VARIANCE MODEL UNDER VARIANCE PRINCIPLE[J].Acta mathematica scientia,Series B, 2015, 35(2): 303-312.

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

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