风险理论在数学分析和概率中的应用  

Some Applications of Risk Theory to Mathematical Analysis and Probability

作　　者：孙国红[1] 张春生[2] 

机构地区：[1]天津农学院基础科学系,天津300384 [2]南开大学数学科学学院,天津300071

出　　处：《南开大学学报（自然科学版）》2010年第2期99-105,共7页Acta Scientiarum Naturalium Universitatis Nankaiensis

基　　金：天津市自然科学基金(08JCYBJC02200);天津市教育科学"十一五"规划课题(G138);973国家基础研究项目(2007CB814905)

摘　　要：应用与Egidio dos Reis完全不同的方法考虑古典风险模型下由每次索赔引起破产的概率,并在去掉安全负荷的影响下得出了一些依赖于拉普拉斯变换的精确表达式.当初始资本为0时,在负的安全负荷情形下,给出了破产经过n次索赔首次恢复到零的概率函数.The classical surplus model the number of claims occurring up to ruin,if it occurs, is considered by a different method presented by Egidio dos Reis.Some finite expressions depending on derivatives for the Laplace transforms are given when the limitation on safety loading is taken off.Finally,when initial surplus is zero,it＇s studied that the calculation of the probability function of the number of claims during a negative excursion of the surplus process in the case of negative safety loading.

关 键 词：安全负荷 破产概率 测度变换 递归计算 

分 类 号：O211.9[理学—概率论与数理统计] F840[理学—数学]