Long-Run Average Reward Maximization of A Regulated Regime-Switching Diffusion Model

TL;DR

This paper develops a numerical method combining Markov chains and neural networks to solve a complex, regulated regime-switching diffusion model for optimal reinsurance, investment, and dividend strategies, ensuring convergence and practical applicability.

Contribution

It introduces an integrated control framework with solvency constraints and a novel approximation scheme for high-dimensional problems involving regime switching.

Findings

The proposed numerical scheme converges to the true optimal value.

The method effectively handles high-dimensional regime-switching models.

Numerical examples demonstrate the approach's feasibility and accuracy.

Abstract

This study considers an optimal reinsurance, investment, and dividend strategy control problem for insurance companies in a regulated Markov regime-switching environment, intending to maximize long-run average reward. Unlike existing single or dual strategy studies, an integrated control framework is established under solvency constraints, allowing investment and dividends only when the surplus process exceeds a minimum cash requirement level. To address the analytical difficulties associated with solving HJB equations and stationary distributions in high-dimensional state spaces under regime switching, we construct a numerical approximation scheme for the optimal strategy function based on Markov chains and neural networks. Furthermore, we establish the convergence of the corresponding sequence of surplus processes and rigorously prove that the associated optimal values converge to the true value function. Finally, we provide a numerical example based on the approximate dynamic programming method to demonstrate the feasibility of the proposed method.