Optimal Control Strategy For Dividend Payments And Reinsurance In The Discrete Sparre Andersen Risk Model

The rapid development of China's economy has brought new opportunities to the insurance industry,and the insurance industry has entered a stage of rapid development.The dividend distribution and risk control of insurance companies are particularly important.This paper mainly considers the discrete Sparre Andersen risk model with dividend payments and reinsurance.The company controls the amounhts of dividends and reinsurance premiums in order to maximize the cumulative expected discounted dividends prior to ruin.In the first chapter,we mainly introduce the research background of optimal dividend and reinsurance,the research status at home and abroad,and the research results of this paper.In the second chapter,firstly,we introduce the basic knowledge of discrete Sparre Andersen risk model,then the introduce reinsurance problem into the model,obtain the ordinary renewal process controlled by dividend strategy and reinsurance strategy,and finally optimizes the value function.In the third chapter,the optimal value function is transformed to simplify the calculation process.In the fourth chapter,we mainly study the properties of the optimal dividend reinsurance policy,and prove the existence and uniqueness of the solution of the optimal value function by using the contraction mapping principle.In the fifth chapter,we mainly study the stochastic simulation of the optimal strategy.According to the random sample generated by the computer or the historical data of the company,we estimate the consistency of the original value function.In the last part of chapter,the above algorithm is explained by numerical example.