Dividend Optimization Problem In The Moving Average Risk Model

In this paper,we discuss the optimal dividend problem in a risk model with dependent claims.The company’s surplus is described by moving average model,and the dividend amounts is controlled to maximize the cumulative expected discounted dividends prior to ruin.The first chapter is the introduction,which first introduces the research background and current situation of this paper,then puts forward the dependent risk model and innovation of this paper,and finally explains the structure of the paper.The second chapter gives the model and basic assumptions,the chapter describes the moving average model,defines the value function and the optimization goal.The third chapter introduces the optimal strategy and the optimal value function.Firstly,we analyze the optimal strategy and deduce the equation satisfied by the optimal value function.Secondly,we give the properties of the optimal strategy,prove two important theorems of the optimal strategy,which will prepare for subsequent reasoning.Finally,we give the algorithm for optimal value function and optimal strategy,that is,an iterative algorithm for solving the optimal strategy is constructed by using the contraction operator,and we give an example for applying the iterative algorithm to calculate the optimal value function and the optimal strategy.The fourth chapter further gives the Gerber-Shiu function under the control of the optimal dividend strategy.The fifth chapter puts forward the idea of dimension reduction.Due to the dependent relationship between the gains of each period,the dimension of the optimal dividend strategy may be too high.Therefore,the chapter discusses how to simplify the strategy and proposes a dimension reduction method.Numerical examples show that the method is effective and the results can be used to approximate the optimal value function and the optimal dividend strategy.The important advantage of this method is that it not only greatly reduces the computation but also reduces the complexity of the strategy so that the strategy is easy to apply.The last part is a summary of this paper,and puts forward the further research direction.