This paper deals with the dividend optimization problem for an insurance company, whose surplus follows a jump-diffusion process. The objective of the
company is to maximize the expected total discounted dividends paid out until the
time of ruin. Under concavity assumption on the optimal value function, the paper
states some general properties and, in particular, smoothness results on the optimal
value function, whose analysis mainly relies on viscosity solutions of the associated
Hamilton-Jacobi-Bellman (HJB) equations. Based on these properties, the explicit
expression of the optimal value function is obtained. And some numerical calculations
are presented as the application of the results.
