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OPTIMAL MEAN–VARIANCE REINSURANCE WITH COMMON SHOCK DEPENDENCE

Part of: Mathematical economics Stochastic systems and control

Published online by Cambridge University Press:  30 August 2016

ZHIQIN MING ,
ZHIBIN LIANG  and
CAIBIN ZHANG
ZHIQIN MING
Affiliation:
School of Mathematical Sciences and Institute of Finance and Statistics, Nanjing Normal University, Jiangsu 210023, PR China email xiaoming011204@qq.com, liangzhibin111@hotmail.com, liangzhibin111@hotmail.com
ZHIBIN LIANG*
Affiliation:
School of Mathematical Sciences and Institute of Finance and Statistics, Nanjing Normal University, Jiangsu 210023, PR China email xiaoming011204@qq.com, liangzhibin111@hotmail.com, liangzhibin111@hotmail.com
CAIBIN ZHANG
Affiliation:
School of Mathematical Sciences and Institute of Finance and Statistics, Nanjing Normal University, Jiangsu 210023, PR China email xiaoming011204@qq.com, liangzhibin111@hotmail.com, liangzhibin111@hotmail.com
*
✉liangzhibin111@hotmail.com
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Abstract

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We consider the optimal proportional reinsurance problem for an insurer with two dependent classes of insurance business, where the two claim number processes are correlated through a common shock component. Using the technique of stochastic linear–quadratic control theory and the Hamilton–Jacobi–Bellman equation, we derive the explicit expressions for the optimal reinsurance strategies and value function, and present the verification theorem within the framework of the viscosity solution. Furthermore, we extend the results in the linear–quadratic setting to the mean–variance problem, and obtain an efficient strategy and frontier. Some numerical examples are given to show the impact of model parameters on the efficient frontier.

Keywords

common shock componentcompound Poisson processstochastic linear–quadratic problemHamilton–Jacobi–Bellman equationproportional reinsurance

MSC classification

Primary: 93E20: Optimal stochastic control
Secondary: 91B30: Risk theory, insurance
Type
Research Article
Information
The ANZIAM Journal , Volume 58 , Issue 2 , October 2016 , pp. 162 - 181
Copyright
© 2016 Australian Mathematical Society 

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