Probabilistic approach to risk processes with level-dependent premium rate
研究了保费率随风险储备增加而趋近净利条件临界值的风险过程，用纯概率方法推导了破产概率的上下界，并发现即使索赔分布是轻尾的，破产概率也可能是重尾的。
We study risk processes with level dependent premium rate. Assuming that the premium rate converges, as the risk reserve increases, to the critical value in the net-profit condition, we obtain upper and lower bounds for the ruin probability; our proving technique is purely probabilistic and based on the analysis of Markov chains with asymptotically zero drift. We show that such risk processes give rise to heavy-tailed ruin probabilities whatever the distribution of the claim size, even if it is a bounded random variable. So, the risk processes with near critical premium rate provide an important example of a stochastic model where light-tailed input produces heavy-tailed output.