Research On The Risk Model With Investment Interest Rate

The development of mathematics and statistics has made great contributions to the progress of human society.The development has also made great contributions in the field of finance and insurance.When people used mathematical methods to analyze the ruin problem,the complex economic problems became simple,and the ruin theory is developed on this basis of mathematics.The mathematical model based on the insurance business process is the main research object of ruin theory,Using statistical methods and stochastic process knowledge to analyze risk models can help decision makers precisely predict the risks and the profit.I consider the property of different risk models with the knowledge of probability theory,stochastic process and differential equation,and try to provide theoretical support for risk management.The main contents and conclusions of this paper are listed as follows:Firstly,the dividend problem of dual risk model with liquid reserve and constant dividend barrier is considered.Depending on the different initial surplus,the integral-differential equations satisfied by the expected discounted dividend payments and boundary conditions are obtained.Then,the explicit solution for the expected discounted dividend payments is provided in the case when the profits follow an exponential distribution.Finally,the integral-differential equations satisfied by the moment generating function of the amount of discounted dividend under different initial surplus are obtained.Secondly,the randomized observation periods for the risk model with interest is considered.Assume that the surplus can be only observed at random observation times,on this basis,the integral-differential equations satisfied by the expected discounted penalty function of the dual risk with interest is obtained through stochastic analysis;Finally,according to the boundary conditions satisfied by the expected discounted penalty function,the explicit solution for the Laplace transform of ruin time is provided.Thirdly,on the basis of the first model,we consider the dividend problem of dual risk model with perturbation.The integral-differential equations satisfied by the moment generating function of the amount of discounted dividend under different initial surplus are obtained.On the one hand,insurance companies need to design different kind of insurance to meet the needs,the development of ruin theory provides theoretical support for the diversity of insurance type.On the other hand,investors are always trying to reduce the probability of loss as far as possible,and seek more benefits,the risk model with different dividend policy and investment can guide investors to make optimal decisions.The dual risk model can explain the unexplained problems in classical risk models,such as life insurance,this model can vividly describe some industries which need continuous cost while the income is uncertain.In conclusion,the research of dual risk model with investment interest rate has strong theoretical foundation and wide practical value.