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OPTIMAL PROPORTIONAL REINSURANCE AND INVESTMENT PROBLEM WITH CONSTRAINTS ON RISK CONTROL IN A GENERAL JUMP-DIFFUSION FINANCIAL MARKET

Part of: Mathematical economics

Published online by Cambridge University Press:  17 February 2016

HUIMING ZHU ,
YA HUANG ,
JIEMING ZHOU ,
XIANGQUN YANG  and
CHAO DENG
HUIMING ZHU*
Affiliation:
College of Business Administration, Hunan University, Changsha 410082, PR China email zhuhuiming@hnu.edu.cn, huangya0219@163.com, dengchaohunan@163.com
YA HUANG
Affiliation:
College of Business Administration, Hunan University, Changsha 410082, PR China email zhuhuiming@hnu.edu.cn, huangya0219@163.com, dengchaohunan@163.com
JIEMING ZHOU
Affiliation:
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, PR China email zhjm04101@126.com, xqyang@hunnu.edu.cn
XIANGQUN YANG
Affiliation:
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, PR China email zhjm04101@126.com, xqyang@hunnu.edu.cn
CHAO DENG
Affiliation:
College of Business Administration, Hunan University, Changsha 410082, PR China email zhuhuiming@hnu.edu.cn, huangya0219@163.com, dengchaohunan@163.com
*
✉zhuhuiming@hnu.edu.cn
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Abstract

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We study the optimal proportional reinsurance and investment problem in a general jump-diffusion financial market. Assuming that the insurer’s surplus process follows a jump-diffusion process, the insurer can purchase proportional reinsurance from the reinsurer and invest in a risk-free asset and a risky asset, whose price is modelled by a general jump-diffusion process. The insurance company wishes to maximize the expected exponential utility of the terminal wealth. By using techniques of stochastic control theory, closed-form expressions for the value function and optimal strategy are obtained. A Monte Carlo simulation is conducted to illustrate that the closed-form expressions we derived are indeed the optimal strategies, and some numerical examples are presented to analyse the impact of model parameters on the optimal strategies.

Keywords

jump-diffusion risk modeloptimal investment strategyproportional reinsuranceexponential utilityHamilton–Jacobi–Bellman equation

MSC classification

Secondary: 91B30: Risk theory, insurance
Type
Research Article
Information
The ANZIAM Journal , Volume 57 , Issue 3 , January 2016 , pp. 352 - 368
Copyright
© 2016 Australian Mathematical Society 

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