Optimal Investment And Dividend Strategy In The Discrete Sparre Andersen Risk Model

In this paper,the author mainly studies how to maximize the expected cumulative discounted dividends of shareholders before bankruptcy by controlling the proportion of dividend payment,venture capital and risk-free investment in the discrete-time Sparre Andersen risk model with investment and dividend payment.The problem not only has the theoretical foundation but also contains the practical significance.In the first chapter,we mainly introduce the relevant research background and research status.Then indicate the research method of this paper and the place of innovation.Finally,we make a brief description for this paper.In the second chapter,the basic knowledge involved in this paper is explained in detail,and reasonable assumptions are given for investment and dividend strategies.At the end,the optimal value function is defined and the optimization objective of this paper is pointed out.In the third and fourth chapter we give the algorithm of the optimal dividend strategy and expression by analyzing a Hamilton-Jacobi-Bellman equation and transforming the value function.Furthermore,the existence of the optimal solution of the transformation function is proved by using contration mapping and fixed point principle.In order to make the calculation easier,the five chapter also proposes an innovative random simulation method for the optimal strategy.First,the sample equation is constructed according to the theoretical model,and then the existence of the optimal solution of the sample equation is proved by analogy with chapter4.In the end,it is proved that the solution of equation is the consistent estimate of the real value,the main mathematical methods of which are the central limit theorem and the law of large numbers.In the six chapter,the random simulation method in the Matlab is used for numerical analysis in an example,which shows the innovative simulation method is a very good and helpful method for making dividend payment and investment decisions.In the last part,we firstly summarize the ideas and results of the paper.Then points out the problems to be considered in the next research and the research significance of these problems.