非标准风险模型的渐近行为：多变量亚指数索赔与恒定利息力
Asymptotics for a nonstandard risk model with multivariate subexponential claims and constant interest force
AI总结：
本文研究了多变量亚指数索赔和恒定利息力的非标准风险模型的渐近行为，推导了有限和无限时间 horizon 下的进入概率结果，并应用于资金链问题。
摘要：
本文研究了某一特定稀有集合的进入概率的渐近行为，考虑了有限和无限时间 horizon。该多变量风险模型由一个共同的计数过程驱动，具有恒定的利率，并允许索赔向量之间的相互依赖性。对于有限时间 horizon，使用了共同索赔向量的多变量亚指数分布和回归依赖的弱依赖结构。对于无限时间 horizon，索赔向量来自一个更小的分布类，且弱依赖结构更为一般。所有结果均在某些关于计数过程矩的额外假设下推导出来，这些假设由所有非均匀 renewal 过程和许多准 renewal 过程分别满足。此外，结果被专门应用于多变量正则变化的情况，其中对折扣累积索赔的进入概率的渐近行为获得了更明确的结果。在本文的最后，所获得的结果被用来研究具有最终布朗运动扰动的风险模型的有限和无限时间 horizon 资金链问题。
英文摘要：
In this paper, the asymptotic behavior of the entrance probability of discounted aggregate claims of a certain family of rare sets is studied, considering the finite and infinite time horizons. This multivariate risk model, driven by a common counting process, has a constant interest rate and allows the interdependence of claim vectors. For the finite time horizon, the multivariate subexponential distribution of the common claim vector and the weak dependence structure of regression dependence are used. For the infinite time horizon, the claim vector is taken from a smaller distribution class, and the weak dependence structure is more general. Both results are derived under some additional assumptions on the moments of the counting process, which is fulfilled by all inhomogeneous renewal processes and many quasi-renewal processes, respectively. Moreover, the results are specialized to the multivariate regularly varying case, where more explicit results on the asymptotic behavior of the entrance probability of the discounted aggregate claims are derived. At the end of the paper, the results obtained are used to study the finite and infinite time horizon ruin problems of a risk model with eventual Brownian perturbations.
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