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Uniform asymptotics for the finite-time ruin probability of a generalized bidimensional risk model with Brownian perturbations
Stochastics ( IF 0.8 ) Pub Date : 2019-12-30 , DOI: 10.1080/17442508.2019.1708362
Dongya Cheng 1
Affiliation  

This paper considers a generalized bidimensional continuous-time risk model with heavy-tailed claims and Brownian perturbations. In this model, the claim sizes from different lines of business are tail asymptotically independent, while the claim-number processes from different lines of business are arbitrarily dependent. Under some moment conditions on the claim-number processes, an asymptotic formula is established for the finite-time ruin probability defined as the probability that the aggregate surplus process goes below zero over the time horizon [ 0 , t ] . The asymptotics holds uniformly for t in some kind of interval. The moment conditions on the claim-number processes are automatically satisfied when the claim-number processes are renewal counting processes. The obtained results confirm that the Brownian perturbations have no influence on the asymptotics of the ruin probability under consideration.



中文翻译:

具有布朗扰动的广义二维风险模型的有限时间破产概率的一致渐近性

本文考虑具有重尾索赔和布朗扰动的广义二维连续时间风险模型。在此模型中,来自不同行业的索赔数量是渐近独立的,而来自不同行业的索赔数量过程则是任意相关的。在索赔数量过程的某些时刻条件下,为有限时间破坏概率建立一个渐近公式,该概率定义为时间范围内总剩余过程低于零的概率 [ 0 Ť ] 。渐近线在某种间隔内均匀地保持t。当权利要求编号过程是续展计数过程时,将自动满足权利要求编号过程的时刻条件。所得结果证实布朗扰动对所考虑的破产概率的渐近性没有影响。

更新日期:2019-12-30
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