The Study Of Ruin Probability In Some Risk Models

With the progress of the times and the enhancement of people's awareness of insurance,the risk theory has become an important research object in the field of mathematics.The Insurance company are concerned not only about their earnings but also about the possibility of bankruptcy and method for reducing bankruptcy risk.Ruin probability has become a quantitative criterion to evaluate whether the insurance company is operating steadily.The study of the ruin probability and the upper bound of the ruin probability is helpful for the insurance company to make a reasonable prediction and its own development.For a long time in the research of risk theory,the former has obtained various kinds of models and upper bound of ruin probabilities.Most of the models are only theoretical research and qualitative analysis,there is no actual data as a support,in practice,the insurance company can not provide effective decision-making.In this paper,based on the existing theories,the paper mainly studies three kinds of risk models and improves and extends them.Due to the practical operation of insurance company will be affected by many uncertain factors,so add disturbance items and the interest rate to the three kinds of risk models and undertake quantitative analysis by numerical simulation,some conclusions are obtained in order to reduce the bankruptcy of insurance companies and provide realistic basis for efficient and stable operations.The first chapter,it introduces the theoretical knowledge of the classical risk model and the related results and significance of this paper,main contents,innovation of this article.The second chapter,preliminaries are introduced,the classical risk model and related results are given,then introduces related theorems and basic knowledge such as compound Poisson process,moment generating function,adjustment coefficient,Brownian motion,negative risk model,Sparre Andersen risk model,reinsurance process and others.The third chapter mainly introduces the negative risk model,considering the disturbance items and constant interest rate,using the Chebyshev inequality to satisfy the model's ruin probability expression and the upper bound for the ruin probability.Finally,it respectively analyzes the the influence of disturbance items and interest rate on ruin probability by using numerical simulation.In the fourth chapter,the ruin probability of Erlang(2) Sparre Andersen risk model is studied,the effects of different premium rates on the ruin probability are analyzed.We found that recursive method is superior to martingale method when different methods are used to estimate the upper bound for the ruin probability.The fifth chapter,the problem about proportional reinsurance risk model with disturbance items is studied,it gives the adjustment coefficient expressions for different distributions,then we can calculate the corresponding upper bounds of ruin probability.Finally,using the numerical simulation analysed the influence of different reinsurance coefficients and different disturbance coefficients on the ruin probability.