Research On Optimal Control Policy Of Insurance Company Based On The Probability Of Drawdown

With the development and improvement of insurance business,insurance company is playing a more and more important role in financial institutions.For insurance company,to manage insurance is a process to manage risks.In order to work stably,insurance company will purchase reinsurance to diversify risks and invest to gain benefits.Therefore,designing optimal reinsurance-investment policy for insurance company is a hot topic in actuarial research.In the research,the optimal control strategy is usually considered to optimize the goal of insurance company,such as minimizing the probability of drawdown.Drawdown can be used to measure a decline in a portfolio from a record high.The smaller the value,the lower risk the insurer faces.In the thesis,the surplus process of insurance company is modeled by jumpdiffusion model.The insurance company consider to purchase excess-of-loss reinsurance,and the optimal control policy is solved based on the objective function of the probability of drawdown.By the technique of dynamic programming and the corresponding HJB equation,we can get the expression of the probability of drawdown as well as the optimal policy.The research is mainly carried out in three parts.In the first part,insurance company considers to invest in a risk-free asset and a risky asset in the financial market,and gets the optimal reinsurance-investment policy.In the second part,we take into account the dependent risk.Insurance company puts wealth into risk-free asset and the optimal reinsurance policy is solved.In the third part,we take the earthquake disasters occurring in the Chinese mainland from 2003 to 2019 as an example.Based on the POT(Peaks Over Threshold)model,we fit the distribution of the economic losses caused by the earthquake disasters and the number of earthquakes in line with the catastrophe level.Later,we combine it with the model in the thesis.