题目:Optimal dividend strategy in dual model with both fixed and proportional transaction costs

摘要:In this paper, we extend the optimal dividend problem studied in Avanzi etc (2007) to the case in presence of transaction costs. Both fixed and proportional costs are considered in the dual risk model. The value function is defined as the expected total discounted dividends up to time of ruin. First, we prove that the value function is linear increasing. And with the linear increasing property, we present the verification theorem for the value function. Then, by solving the quasi-variational inequalities associated to this optimal problem, we obtain the classical solutions to both value function and optimal dividend strategy when the income sizes follow a common exponential distribution. In presence of the fixed cost, it is showed that the optimal strategy is a two-barrier policy, and the optimal barriers are only impacted by the fixed cost but independent of the proportional cost. A numerical example is given in the end of this paper. It displays that the fixed cost has a significant impact on the optimal dividend strategy and the value function as well. The increased fixed cost results into larger but less frequent dividend payments.