索赔盈余风险模型中精确大偏差

Precise large deviations for claim surplus risk model

考虑了控制变化族(D族)上索赔过程与保费过程构成的索赔盈余风险模型,研究了此风险模型中带相依关系的随机变量的非随机和与随机和的尾概率渐近问题,利用求相依不同分布的随机变量的非随机和与随机和的精确大偏差方法,得到了带上延拓负相依和混合相依关系的不同分布的随机变量构成的索赔风险模型中的非随机和与随机和的精确大偏差渐近的结论,最后建立了索赔盈余风险模型中精确大偏差的渐近公式.

The claim surplus risk model with dominated variation class（class D）including claim process and premium process,is considered.The asymptotic behavior of the tail probabilities of nonrandom sum and random sum of dependent random variables in the claim surplus risk model is studied,and some asymptotic results about the precise large deviations for non-random sum and random sum of upper extended negatively dependence and-mixing dependent random variables in the claim risk model are got by using the methods of precise large deviations for non-random sum and random sum of dependent and non-identically distributed random variables.Finally,the asymptotic formula of precise large deviation in the claim surplus risk model is obtained.