| The risk theories, be an importance part that the insurance or acturial calculate mathematics, the research object is the random model of the insurance business and bankrupt all rate.Compound Poisson the risk model of the classic is a kind of basic model.In this kind of model, the insurance company receives the insurance policy that a fixed amount has the same fee rate.But in fact,it is not each insurance policy will cause the claim, the quantity that claim thus will is the son quantity( can think thus) of the insurance policy quantity, and, because of the market reason, the quantity of each insurance policy is also not same, is same insurance policy of type, so we can see it as random variable sequence which has the same mean, and suppose it obey same distribute.Because the market has the influences of other factors, an above-mentioned factor of income of the insurance company should still be interference by other factors, we establish the interference factor as Brownian motion, according to this fact, expanding a new model to compound Poisson risk model of the classic. The investigation insurance policy arrives the process in this model is together a Poisson process, the reason compensates to take place the process also is a Poisson process . the risk surplus model of a Poisson processR, = u+First, we under the condition of two kinds of assumption, get the Lundberg inequality of ruin probability,and give explicit expressions for the ruin probability .Later on, we compared various similar situation next, the size of the Lundberg exponent, it as a result matches us in advance of guess.On this foundation, we made some expansion : Expand the category of the insurance policy to the multiple.(in the text is n dimension, it is similar to the abocve).Because that model matches the insurance company more in conduct process of actual condition, thus make textual research as a result had the stronger actual application value. |
