Numerical solutions of optimal risk control and dividend optimization policies under a generalized singular control formulation

This paper develops numerical methods for finding optimal dividend pay-out and reinsurance policies. A generalized singular control formulation of surplus and discounted payoff function is introduced, where the surplus is modeled by a regime-switching process subject to both regular and singular controls. To approximate the value function and optimal controls, Markov chain approximation techniques are used to construct a discrete-time controlledMarkov chain. The proofs of the convergence of the approximation sequence to the surplus process and the value function are given. Examples of proportional and excessof-loss reinsurance are presented to illustrate the applicability of numerical methods. © 2012 Elsevier Ltd. All rights reserved.