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

Authors:
Zhuo Jin;G. Yin;Chao Zhu
Affiliations:
Centre for Actuarial Studies, Department of Economics, The University of Melbourne, VIC 3010, Australia;Department of Mathematics, Wayne State University, Detroit, MI 48202, United States;Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI 53201, United States
Venue:
Automatica (Journal of IFAC)
Year:
2012

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Abstract

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 controlled Markov chain. The proofs of the convergence of the approximation sequence to the surplus process and the value function are given. Examples of proportional and excess-of-loss reinsurance are presented to illustrate the applicability of numerical methods.