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  • OPTIMAL MEAN–VARIANCE REINSURANCE WITH COMMON SHOCK DEPENDENCE

  • Part of
  • ZHIQIN MING, ZHIBIN LIANG, CAIBIN ZHANG
  • Journal:
    The ANZIAM Journal / Volume 58 / Issue 2 / October 2016
    Published online by Cambridge University Press:
    30 August 2016, pp. 162-181
    • Article
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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.