中文摘要：

比较了经典风险模型（即Cramer-Lundberg模型）与现代风险模型，在小额索赔条件下，利用离散嵌入技术、随机游动方法和鞅方法获得了现代风险模型破产概率的指数型上界，并使用MATLAB数值模拟验证了结论的有效性．本文结果可为现实中保险公司的风险控制与初始保证金界定提供理论依据．

英文摘要：

This paper compares the classical Cram＆-Lundberg Model with the modem risk model. Under the small claim condition, it derives an exponential upper bound of ultimate ruin probability for the modem risk model by a comprehensive application of embedding technology of stochastic processes, random walks method and martingale approach. A MATLAB numerical simulation is also provided to show the effectiveness of our result. This work provides a theoretical basis for risk controlling as well as initial capital rating for the realistic insurance companies.