Study On Some Problems Of Optimal Dividend And Capital Injection In Lévy Risk Process

With the rapid development of global economy,finance,science and technology,the cooperation among countries in trade,finance and other industries has become more and more frequent.Dividend and capital injection has always been a hot topic in the field of Finance and insurance.Therefore,it is necessary to find a model that is more consistent with the actual operation of the financial market.Because the process is independent,stable and incremental,Markov,none Poor separability and other good properties.It can be more in line with the actual simulation of the financial market operation law,a good description of the asset operation process.In addition,the sample path of the process has discontinuities,which can describe the jump behavior in the price movement of financial assets.Based on the above reasons,the process is widely used in related research fields by the academic community.This paper adopts more in line with the actual too The process risk model studies the joint optimal problem under dividend and capital injection strategies.The specific research contents are as follows(1)This paper studies the optimal dividend problem with proportional transaction cost and fixed cost in the process risk model under the refraction and reflection barrier strategy.By using the scale function transformation,the Integro differential equation of the total expected discount of dividend satisfying the constraint conditions is given.Through the derivation of the smoothness and differentiability of the value function,the optimal strategy satisfied by the value function and the maximum value of the value function are found Its existence and related properties.(2)This paper studies the joint optimal dividend problem with impulse dividend and capital injection cost in the process risk model under the periodic barrier expansion strategy.By using the scale function transformation,the integral differential equation of the total expected discount of the dividend minus the difference of capital injection satisfying the constraint conditions is given.Through the derivation of the smoothness and differentiability of the value function,the optimal strategy and its enabling value function satisfied by the value function are found out.