Optimal Reinsurance and Dividend Strategies Under the Markov-Modulated Insurance Risk Model

In this article, we consider the optimal reinsurance and dividend strategy for an
insurer. We model the surplus process of the insurer by the classical compound
Poisson risk model modulated by an observable continuous-time Markov chain. The
object of the insurer is to select the reinsurance and dividend strategy that maximizes
the expected total discounted dividend payments until ruin. We give the definition of
viscosity solution in the presence of regime switching. The optimal value function
is characterized as the unique viscosity solution of the associated Hamilton–Jacobi–
Bellman equation and a verification theorem is also obtained.