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

This paper investigates insurance surplus management under strict regulatory constraints and market regime switching. The objective is to maximize the long-run average reward in a regulated regime-switching diffusion model. We establish a joint optimization framework to coordinate reinsurance, investment, and dividend strategies. Distinct from existing literature, we introduce specific regulatory threshold constraints, under which risky investment and dividend distribution are permitted only when the surplus exceeds minimum capital requirement. The coupling of these hard boundary constraints with the high-dimensional regime-switching environment leads to high nonlinearity and non-smoothness in the Hamilton-Jacobi-Bellman equations. This poses significant challenges for analytical derivations, thus we construct a theoretical framework based on Markov chain approximation, and we employ a deep neural network algorithm to efficiently handle the irregularity of the value function caused by regulatory thresholds. We establish the convergence of the approximating sequences to the risk model, as well as the approximate value function converges to the true value function. Finally, numerical examples validate the effectiveness of our method and analyze the performance of optimal strategies