Stochastic optimal control on impulse dividend model with stochastic returns

This paper investigates a stochastic optimal control problem by the impulse dividend model with stochastic returns. To search for its candidate solution, we propose a series of quasi-variational inequalities (QVI), for which an analytic solution composed of a power series is provided. Moreover, some properties, such as the uniqueness of uncertain parameters and partition points, of the solution are also verified under some conditions. The procedure on how to calculate unknown parameters is also presented. Theorematic analysis verifies that the policy based on the proposed solution is just the optimal dividend policy.