Optimal dividend control of an impulse model with stochastic risk exposure

In this paper, we consider a new dividend model in which the diffusion term representing risk exposure follows a special stochastic process. We transform the problem into the quasi-variational inequalities (QVI). The optimal solution and control for the QVI are obtained and verified, which are equal to the ones of the proposed model respectively. The most important contribution of this paper is that the optimal dividend amounts are proved to have stochastic values under some rules, different from previous models with discrete and fixed dividend amounts at each dividend event. A numerical example is provided, the results of which are in accordance with the theoretical analysis.