The Dividend Problem Of Two Dimensional Dual Model

In this paper,we study the dividend of the two-dimensional dual model with diffusion.Taking the influence of the external environment into account,we consider the two-dimensional dual model with diffusion.The company choices the barrier or threshold dividend strategy to control the surplus,which aims at maximizing the expected present value of dividends until ruin.Firstly,we consider the two-dimensional dual model with diffusion under a barrier dividend strategy,by solving the corresponding Hamilton-Jacobi-Bellman(HJB)equation,we obtain the optimal dividend strategy of the problem.We also derive explicit results when the two gains follow different exponential distribution.Then,we study the two-dimensional dual model with diffusion under a threshold dividend strategy,We obtain a group of integro-differential equations satisfied by the expected total sum of discount dividends until ruin.And explicit results when the gains of the two projects are exponentially distributed are derived.By applying the method of the Laplace transform we obtain the case where gains follow general distributions.We also illustrate how to calculate the optimal dividend threshold.