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The present paper addresses the issue of the stochastic control of theoptimal dynamic reinsurance policy and dynamic dividend strategy, which arestate-dependent, for an insurance company that operates under multipleinsurance lines of business. The aggregate claims model with athinning-dependence structure is adopted for the risk process. In theoptimization method, the maximum of the cumulative expected discounted dividendpayouts with respect to the dividend and reinsurance strategies are consideredas value function. This value function is characterized as the smallest superViscosity solution of the associated Hamilton-Jacobi- Bellman (HJB) equation.The finite difference method (FDM) has been utilized for the numerical solutionof the value function and the optimal control strategy and the proof for theconvergence of this numerical solution to the value function is provided. Thefindings of this paper provide insights for the insurance companies as suchthat based upon the lines in which they are operating, they can choose a vectorof the optimal dynamic reinsurance strategies and consequently transfer somepart of their risks to several reinsurers.

Stochastic optimization of the Dividend strategy with reinsurance in correlated multiple insurance lines of business