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OPTIMAL INVESTMENT AND REINSURANCE IN A JUMP DIFFUSION RISK MODEL

Published online by Cambridge University Press:  14 October 2011

XIANG LIN  and
PENG YANG
XIANG LIN*
Affiliation:
School of Mathematical Science and Computing Technology, Central South University, No. 22 South Shaoshan Road, Changsha 410075, Hunan, PR China (email: xlin@csu.edu.cn, yangpeng511@163.com)
PENG YANG
Affiliation:
School of Mathematical Science and Computing Technology, Central South University, No. 22 South Shaoshan Road, Changsha 410075, Hunan, PR China (email: xlin@csu.edu.cn, yangpeng511@163.com)
*
✉For correspondence; e-mail: xlin@csu.edu.cn
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Abstract

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We consider an insurance company whose surplus is governed by a jump diffusion risk process. The insurance company can purchase proportional reinsurance for claims and invest its surplus in a risk-free asset and a risky asset whose return follows a jump diffusion process. Our main goal is to find an optimal investment and proportional reinsurance policy which maximizes the expected exponential utility of the terminal wealth. By solving the corresponding Hamilton–Jacobi–Bellman equation, closed-form solutions for the value function as well as the optimal investment and proportional reinsurance policy are obtained. We also discuss the effects of parameters on the optimal investment and proportional reinsurance policy by numerical calculations.

Keywords

jump diffusion risk modelproportional reinsuranceinvestmentcompound Poisson processexponential utilityHamilton–Jacobi–Bellman equation

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 52 , Issue 3 , January 2011 , pp. 250 - 262
Copyright
Copyright © Australian Mathematical Society 2011

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