Stochastic optimization of the Dividend strategy with reinsurance in correlated multiple insurance lines of business
The present paper addresses the issue of the stochastic control of the optimal dynamic reinsurance policy and dynamic dividend strategy, which are state-dependent, for an insurance company that operates under multiple insurance lines of business. The aggregate claims model with a thinning-dependence structure is adopted for the risk process. In the optimization method, the maximum of the cumulative expected discounted dividend payouts with respect to the dividend and reinsurance strategies are considered as value function. This value function is characterized as the smallest super Viscosity solution of the associated Hamilton-Jacobi- Bellman (HJB) equation. The finite difference method (FDM) has been utilized for the numerical solution of the value function and the optimal control strategy and the proof for the convergence of this numerical solution to the value function is provided. The findings of this paper provide insights for the insurance companies as such that based upon the lines in which they are operating, they can choose a vector of the optimal dynamic reinsurance strategies and consequently transfer some part of their risks to several reinsurers.