Dividend Maximization when Cash Reserves Follow a Jump-Diffusion Process (Communications in Mathematical Research, 2021)
This paper deals with the dividend optimization problem for an insurance company, whose surplus follows a jump-diffusion process. The objective of thecompany is to maximize the expected total discounted dividends paid out until thetime of ruin. Under concavity assumption on the optimal value function, the paperstates some general properties and, in particular, smoothness results on the optimalvalue function, whose analysis mainly relies on viscosity solutions of the associatedHamilton-Jacobi-Bellman (HJB) equations. Based on these properties, the explicitexpression of the optimal value function is obtained. And some numerical calculationsare presented as the application of the results.
Keywords: jump-diffusion model; dividend payment; Hamilton-Jacobi-Bellman equation; viscosity solution.