Study On The Ruin Probability In Three Kinds Of Generalized Risk Models

Ruin theory which is also called risk theory, is the core content of the category of the insurance mathematics. Cramer and Lundberg approved the classical risk model as follows: the number of individual claims from an insurance portfolio is assumed to follow a Poisson process.The individual claim sizes are independent and identical random variables, and the premiums are described by a constant rate. In this kind of model, under the consumption of the claims follow exponentially distributed they finally obtained the explicit expressions of ruin probability.Based on the classical risk model, a series of risk model which can better describe the practical operation of insurance company has been extended by many scholars. I consider many factors on the basis and use relevant theory about stochastic processes and risk theory to research the ruin probabilities of insurance company. In detail, three aspects of content are considered.1,We get a compound Poisson—Geometric Process Risk Model that is perturbed by diffusion. In the classical risk model the number of individual claims from an insurance portfolio is assumed to follow a Poisson process, we consider another kind of compound Poisson-Geometric model which can better describer the practical operation of insurance company, Furthermore, we consider this model perturbed by diffusion. In this kind of model we finally obtain the renewal equations which the probability of ruin and the probability of survival satisfy, under the consumption of the claims follow exponentially distributed we finally obtain the explicit expressions of ruin probability and survival probability, and also the Adjustment coefficient.2,Inspired by K.Borch, Based on the Classical Risk Model and reinsurance theory, this paper considers the ruin probabilities of n-Company stop loss-proportional mixed reinsurance, under the assumptions that the claims are exponentionally distributed the expressions for the ruin probabilities and adjustment coefficient of n-Company are obtained, this results prove the important memoryless property of the Exponential Distribution, and at last we discuss the effects of reinsurance of reinsured company and how to improve it.3,This paper researches ruin probabilities of insurance company and reinsurance company with diffusion terms, Under the assumptions that the claim has a Erlang(2) distribution. The relationship between deductible and the corresponding ruin probabilities is obtained .The results not only extended Francois and Gerber's corresponding results for classical Cramer-Lundberg risk model, but also have the actual value on the background of Revenues of insurance company having the rights to purchase risky assets.