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RUIN PROBABILITIES UNDER AN OPTIMAL INVESTMENT AND PROPORTIONAL REINSURANCE POLICY IN A JUMP DIFFUSION RISK PROCESS

Part of: Stochastic processes Mathematical economics

Published online by Cambridge University Press:  09 March 2010

YIPING QIAN  and
XIANG LIN
YIPING QIAN
Affiliation:
School of Business, Central South University, Yuelu Mountain, Changsha 410083, Hunan, PR China
XIANG LIN*
Affiliation:
School of Mathematics, Central South University, No. 22 South Shaoshan Road, Changsha 410075, Hunan, PR China (email: xlin@csu.edu.cn)
*
✉For correspondence; e-mail: xlin@csu.edu.cn
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Abstract

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In this paper, we consider an insurance company whose surplus (reserve) is modeled by a jump diffusion risk process. The insurance company can invest part of its surplus in n risky assets and purchase proportional reinsurance for claims. Our main goal is to find an optimal investment and proportional reinsurance policy which minimizes the ruin probability. We apply stochastic control theory to solve this problem. We obtain the closed form expression for the minimal ruin probability, optimal investment and proportional reinsurance policy. We find that the minimal ruin probability satisfies the Lundberg equality. We also investigate the effects of the diffusion volatility parameter, the market price of risk and the correlation coefficient on the minimal ruin probability, optimal investment and proportional reinsurance policy through numerical calculations.

Keywords

ruin probabilityproportional reinsuranceoptimal investment policyLundberg’s equalityHamilton–Jacobi–Bellman equation

MSC classification

Secondary: 60G99: None of the above, but in this section 91B30: Risk theory, insurance
Type
Research Article
Information
The ANZIAM Journal , Volume 51 , Issue 1 , July 2009 , pp. 34 - 48
Copyright
Copyright © Australian Mathematical Society 2010

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