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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*
Affiliation:
School of Mathematical Science and Computing Technology, Central South University, No. 22 South Shaoshan Road, Changsha 410075, Hunan, PR China (email: [email protected], [email protected])
PENG YANG
Affiliation:
School of Mathematical Science and Computing Technology, Central South University, No. 22 South Shaoshan Road, Changsha 410075, Hunan, PR China (email: [email protected], [email protected])
*
For correspondence; e-mail: [email protected]
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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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2011

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