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OPTIMAL MEAN–VARIANCE REINSURANCE WITH COMMON SHOCK DEPENDENCE

Published online by Cambridge University Press:  30 August 2016

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
Corresponding
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Abstract

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.

Type
Research Article
Copyright
© 2016 Australian Mathematical Society 

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