Optimal mean-variance reinsurance with common shock dependence

Zhiqin Ming, Zhibin Liang, Caibin Zhang

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.


doi:10.1017/S144618111600016X

Keywords


common shock component, compound Poisson process, stochastic linear–quadratic problem, Hamilton–Jacobi–Bellman equation, proportional reinsurance.



DOI: http://dx.doi.org/10.21914/anziamj.v58i0.9233



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.