Estimations Of Optimal Dividend Strategy And Gerber-Shiu Penalty Function In A Risk Model With Delayed Claims

In this paper,we mainly study how to estimate the expectation of cumulative discounted dividend before ruin in the discrete-time risk model with delayed claims by the sample data or historical data.With the help of the sample data,we have constructed the consistent estimator of the optimal dividend policy and researched the Gerber-Shiu penalty function under the control of the optimal strategy.The topic is intersting and has a strong practical significance.The first chapter is the introduction part,which first introduces the relevant research background and current situation in detail,then leadsdraw forth the research content and innovation ideas of this paper.Finally,we explain the rest of the structure of this paper.The second chapter is the preparatory knowledge,which constructs the model reasonably and defines the optimization objective.At the end,the related important definitions and lemmas are stated.The third chapter is the focus of this paper.In this chapter,we have constructed a stochastic operator and analyzed the properties of the operator successfully,and proved three important theorems related to it.In the fourth chapter,the equation of value function is analyzed,and the expression of optimal dividend strategy is deduced theoretically.Finally,combining with the content of the third chapter,we propose a consistent estimation of the optimal dividend strategy.In the fifth chapter,we further consider the estimation of Gerber-Shiu penalty function under the control of optimal dividend strategy.The sixth chapter is given for numerical calculation.Firstly,an example of insurance is given.With the help of MATLAB software,we have generated the random sample data to replace the historical data,and calculated the estimated value of the optimal dividend strategy and compare it with the theoretical value.Secondly,we evaluate the estimation method in the end.Finally,on this basis,the ruin probability under the control of the optimal dividend strategy is calculated(an important special case of Gerber-Shiu penalty function).The last part is a summary of the ideas and main conclusions of this paper,and points out the shortcomings and possible improvement direction of this paper.