Risk Model With Transaction Cost In Markovian Environment

In the process of investing in insurance companies,the purchase and sale of stocks(risk assets)is required commission,stamp duty,transfer fees,that means buying and selling stocks are subject to proportional transaction cost-s.Especially when you have frequent transactions,the all transaction costs of investors are very large.Therefore,this paper studies the impact of transac-tion costs on insurance companies,dividends and ruin probability.At the same time,in order to depict the market environment,insurance companies,invest-ment transactions are conducted in the Markovian environment.The insurance company's surplus is simulated by the Markov-modulated risk model,which takes into account transaction costs when buying and selling risky assetsBased on the above models and assumptions,we obtained the delay integro-differential equations and boundary conditions which satisfied by the expect-ed discounted dividend under the threshold dividend strategies and the delay integro-differential equation and boundary conditions which satisfied by the expected discount penalty function.Because the complexity of the above e-quation,it is difficult to find its display solution.By using the Sine numerical method,we get the similar solution of those equation.Through Matlab we get some pictures,then we discusses the impact of transaction costs on insurance companies,dividends and ruin probability in the Markovian environment.