Numerical Solutions of Optimal Risk Control and Dividend Optimization Policies under A Generalized Singular Control Formulation

TL;DR

This paper introduces numerical methods for optimizing dividend and reinsurance policies using a generalized singular control framework with regime-switching surplus processes, ensuring convergence and applicability through Markov chain approximations.

Contribution

It develops a novel numerical approach for solving complex surplus control problems with regime-switching dynamics, extending existing methods to a more general setting.

Findings

Convergence of the approximation sequence to the true surplus process.

Effective numerical methods demonstrated through reinsurance policy examples.

Applicability to various reinsurance structures like proportional and excess-of-loss.

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 are 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 with two components. 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 the numerical methods.