NUMERICAL METHODS FOR DIVIDEND OPTIMIZATION USING REGIME-SWITCHING JUMP-DIFFUSION MODELS

This work develops numerical methods for finding optimal dividend policies to maximize the expected present value of dividend payout,
where the surplus follows a regime-switching jump diffusion model and the
switching is represented by a continuous-time Markov chain. To approximate
the optimal dividend policies or optimal controls, we use Markov chain approximation techniques to construct a discrete-time controlled Markov chain
with two components. Under simple conditions, we prove the convergence of
the approximation sequence to the surplus process and the convergence of the
approximation to the value function. Several examples are provided to demonstrate the performance of the algorithms.