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Optimal Dividend Payouts Under Jump-Diffusion Risk Processes

This article considers the dividend optimization problem for an insurer with a jump-diffusion risk process in the presence of fixed and proportional transaction costs. Due to the presence of a fixed transaction cost, the mathematical problem becomes an impulse stochastic control problem. Using a stochastic impulse control approach, we transform the stochastic control problem into a quasi-variational inequality for a second-order nonlinear integro-differential equation. Under a risk-neutral assumption for the insurer, we solve this problem explicitly and construct the value function together with the optimal policy. Finally, we discuss the expected time to the first dividend payment when the optimal strategy is employed.