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

Published online by Cambridge University Press:  17 February 2016

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
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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.

MSC classification

Type
Research Article
Copyright
© 2016 Australian Mathematical Society 

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