Optimal Dividend And Capital Injection In A Two-dimensional Dual Risk Model

Dual risk model describes the asset operation process of insurance investment company.With the rapid development of economy,many problems appear in financial insurance investment,such as when to pay dividends and when to inject capital.Therefore,many experts and scholars for insurance investment of dual model gave the extremely high enthusiasm,but most of the researches are based on one-dimensional dual model,two-dimensional dual model of the optimal dividend and capital problem remains to be further research.In this paper,the optimal dividend problem of the existing two-dimensional dual risk model is based,and the optimal dividend and capital injection problems in the two-dimensional dual model is considered.On this basis,the following contents are mainly studied:(1)Considering the two dimensional dual risk model of diffusion and the relativity of two kinds of benefit of restricted dividend and capital injection problem.In order to prevent the company from bankruptcy,we inject capital.Maximizing discounted dividend minus the punished discount.By giving restrictions on dividend and capital injection in the model problem of HJB equation(Hamilton-Jacobi-Bellman equation),proves that the optimal strategy is a threshold strategy,and gets in the limit of the difference between the discounted dividends and capital injection of the integro-differential equation for the discount expectations,and gains on solution of this equation to obey exponential discount when expectations explicit expression.(2)Considering two compound Poisson process of surplus of cooperation through mutual fund investment company of two-dimensional dual model of the optimal dividend and capital problem,aims to maximize discounted dividend weighted sum and minus the discounted penalized weighted sum.Obtained the optimal strategy is a barrier strategy by showing that the optimal value function for the viscosity solution of HJB equation,and gives the numerical iteration method to approximate the value function.(3)Considering the capital exchange agreement and the threshold dividend strategy of the dual risk model for two companies get a description of expected dividend discount integral partial differential equations.The integral-partial differential equations are converted into partial differential equations by differential operators.Finally,the finite element difference method is used to obtain the difference scheme of the equation.