Ruin Probability For A Class Of Risk Model With Multi-claim

In the actual insurance business,the insurance company usually runs multiple insur-ance businesses,and many of which involves multiple claim cases.Starting from this,we consider some risk models with multiple claim cases,the main contents are as follows:(1)we consider a risk model with one insurance business which involves multiple claim cases.We assume that the income counting process is Poisson process,and the claim counting processes are p-sparse processes of the income counting process.The existence and uniqueness of adjustment coefficient is proved first,then Lundberg inequality and the generalized expression of ruin probability are obtained by using martingale inequality and properties under the assumed model.(2)we consider a risk model with multiple insurance businesses,and each of which involves multiple claim cases.First,we derive Lundberg inequality and the generalized expression of ruin probability;Second,claim cases in small enough interval are analyzed,then the integro-differeential equation for survival probability is obtained by transforming model and using total probability formula;Finally,based on the preceding integro-differential equation and the results in classical risk theory,the explicit expression of ruin probability is given under a certain conditions that the risk model has two insurance businesses and claims follow the exponential distributions.(3)we consider a risk model with two dependent insurance businesses.In the previous sections,we assume claim counting processes are Poisson process,and we derive Lundberg inequality and the generalized expression of ruin probability,the integro-differential equation for survival probability,the explicit expression of ruin probability under claims following the exponent ial distributions.In the last section,dependent parts of the original risk model are transformed,and some results on ruin probability are obtained.