The Expected Present Value Of Dividends And Risk Quantities In The Compound Binomial Dual Model With Constant Dividend Barriers

Our study is based on a compound binomial dual model with completely discrete variables.Under the dividend barrier strategies,we discuss the dividend,ruin probability and the time of ruin.The details are as follows.The first chapter is the introduction of the article.We mainly introduce the research background of the paper.In addition,it also introduces the problems to be solved and the structure of the article.Chapter 2 is the introduction of some preliminary knowledge,including models and basic assumptions,contractive mapping theory,etc.Among them,contractive mapping theory is an important theory throughout the whole paper.Chapter 3 is the study on the expected present value of the company's dividends under the barrier strategy.Firstly,under the single barrier strategy,We analyze all possible scenarios at the time of the company's first earnings and time 1.Starting from the two different renewed time points,two different equations of expected present value of dividends are established respectively.Subsequently,under a double-barrier strategy,we establish the equations for the expected present value of dividends under different initial surpluses.We prove that the solutions of these equations are all unique and can be obtained approximately.The main method for proof is to construct related operators on a complete distance space,and prove that the operators are all contractive mappings by using the fixed point principle.Chapter 4 is about the calculation of risk quantities.We mainly study the ruin probability and the expected time of ruin.Taking the time point of the company's first income as the renewed time point,the equation of the ruin probability is established,and the solution is proved to be 1.At the same renewed point,the equation of the expected value of company ruin time is also established.We prove that the solution of the equation is unique and can be obtained approximately.Chapter 5 is the empirical part of this paper.In this chapter,we use the algorithms we provide to give three numerical examples.From the numerical results,we can see that the results of expected present value of dividends from two algorithms are the same.