Research On Some Risk Model Under The Threshold Dividend Strategy

Insurance companies are closely related to people’s lives, which to a certain extent, are the protection of people’s lives, bearing the economic losses caused by the extreme events.The normal operation of the insurance company is influenced by many factors, such as the number of insurance、claim factor, and so on. Risk theory is the theory based on the insurance company’s surplus to study the related ruin problems of the company with the method of probability theory.The initial risk theory is established under ideal conditions, which premiums are received continuously and the claim arrival intensity is constant. As the stochastic phenomenon is deeply understood by people, methods of stochastic phenomenon study continues improving, the risk model becomes more reality. The main improvements are the following three aspects:(1) change its claims process to other renewal process. (2) change the constant income of unit premium to variable as the real premium rate is changed by some factors.(3) consider the actual operation of the risk model with the dividend、interest rate and other factors.In this paper, based on many results of other people, considers the process of claim arrival、the dividend and interest rate factors, then mainly studies the three different risk models:Erlang(n) risk model、Cox model and conditional Poisson risk model. As the process of claim arrival is a random process, the method used in risk theory is mainly based on the probability field, such as the random process、risk theory and probability theory.As the insurance company’s insurance is different, the types of insurance claims arrival process varies. The time interval distribution of Tsunami and earthquake described by the Sparre Andersen risk model is better than described by other models, Cox risk model is more appropriate for the medical field, a Poisson model can be applied to the analysis of the drunk driving accident. With a suitable model to describe the risk, the company’s bankruptcy issues and business prospects of the estimates are more conducive for people to control the risk.This paper first introduces the background and significance of the risk theory, including the research status of domestic and overseas. Secondly, on the basis of the classical risk model, the extended Erlang (n) risk model, in which the distribution of the claim interval time distribution is no longer exponential distribution. In this model, the equation of the penalty function under the constant dividend is obtained by using the method of differential, so as the function under the constant interest rate and constant dividend. For the Cox risk model, the claim arrival intensity is related to the time, the martingale method is used to study a boundary of the ruin probability under the linear dividend, so as the boundary under the interest rate and linear dividend. Finally, a conditional Poisson risk model, the claim arrival intensity of which is a variable, in this model the martingale method is used to study a boundary of the ruin probability under the linear dividend model, so as the boundary under the interest rate and linear dividend.