Abstract：According to the actual situation,we assume that the arrival process of claim,insurance policy and refunding are independent random variables. A practical risk model with a refunding process is introduced, and the arrival of the term policies,the occurrences of claim and refunding are compound binominal processes. By defining the adjustment coefficient and applying a progressive average method and Chebychev inequality,the formula of ultimate ruin probability is proved simply,and a Lundberg inequality is derived.

Keyword：compound binominal risk model;refund;ruin probability;risk model;