Abstract:

 In this paper,we study a risk model of two type claims under a time-dependent ruin bound,where one term policy’s arrival intensity follows a Poisson process of parameterλand its refunding,its abnormal claims and normal claims are respectively relate to the policies ofρ₁-thinning process,ρ₂-thinning process andρ₃ -thinning process,while the other term policy and claim arrival both follow the compound negative binomial distribution.For the risk model we investigate the properties of the surplus process by applying the martingale approach and derive the formula of ruin probability and the Lundberg inequality.

Key words: Ruin bound, Refund, Thinning process, Poisson Process, Compound negative binomial distribution, Ruin probability, Lundberg inequality