Optimal Dividend Problem With Stochastic Dividend Time In Compound Binomial Model

In this paper,we study the optimal dividend problem with stochastic dividend times in compound binomial model.This study is a further development of the periodic optimal dividend problem.Taking the dividend method of random dividend time can make the company pay dividend under the appropriate surplus,and avoid missing the best dividend opportunity to ensure the maximization of shareholders' interests.This research is of great significance both in theory and practice.The first chapter is the introduction.In this chapter,we mainly introduce research background,research content and article structure.The second chapter is the preparatory knowledge.Firstly,some reasonable assumptions are put forward,and the basic model is constructed.Then the optimal value function and the optimization objective is defined.Finally,the relevant definitions and theorems involved in this paper are introduced.In the third chapter,we study the optimal value function and optimal dividend policy with dividend upper bound.Firstly,we construct Hamilton-JacobiBellman(HJB)equations according to various situations of dividend events.Then,it is proved that the equation has a unique bounded solution by the value function transformation method and the fixed point principle,and the Bellman recursive algorithm is provided to solve the equation.Finally,the optimal dividend strategy for a special case where the dividend inter-occurrence times is less than a constant(6 is considered.In the fourth chapter,we analyze the HJB equation of the optimal dividend policy when there is the bankruptcy penalty but without the restriction of dividend upper bound.In this chapter,we use the method similar to the third chapter to construct the HJB equation,and provide the Bellman recursive algorithm for solving the optimal dividend policy and value function.The fifth chapter introduces the stochastic simulation method of optimal strategy and optimal value function.In this chapter,we construct random operators related to the amount of claims,and it is proved that the operator is contractive and its fixed point is the consistent estimate of the solution of the general equation in Chapter 3.Chapter six gives an example of numerical calculation.this example is carried out for the following four cases: Considering the upper bound of dividend,the dividend inter-occurrence times less than a constant (6,with the constraint of bankruptcy penalty and constructing a random operator on the amount of claim.Then a corresponding analysis based on the actual situation was made.The last part summarizes the thoughts and main conclusions of this article,and points out the next improvement direction.