Basic Properties Of The Negative Risk Model And Its Extended Model With Applications

With the development of the insurance,a type of risk process has arisen which is different from the classical risk process,is called negative risk process.In order to describe this type of risk process relevantly,we introduced the negative risk model at the beginning of this thesis, next we considered the constant interest influence to the negative risk model,and then,the model which both contains positive and negative risk processes was established.Under the different models,we mainly resolved the following issues:(1) By using the definition and properties of the moment generating function,we discussed main properties of the negative risk model,derived the expression of the ruin probability and its upper bounder,and obtained expenditure c per unit time by using the Exponential Principle, compared with the one which is obtained in general case.(2) We established the negative model with constant interest,derived the expression of the ruin probability by using the martingale method,through numerical analysis we draw the curves of the ruin probability changed with the constant interest.(3) The model which both contains positive and negative risk processes was discussed, through analyzing we obtained the expression of the ruin probability and compared with the model which the positive risk process and the negative risk process are uncorrelated,obtained the relevance response to ruin probability by numerical example.(4) By using the martingale method,we obtained the explicit of the T's conditional expectation that T is the ruin time of the negative and its extended model.