发表机构
University of the Aegean（爱琴海大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文扩展了非更新驱动的二元风险模型，在相依计数过程下研究折现总索赔联合尾部的渐近行为，推导出不同分布类下的显式表达式，并揭示多元非线性单大跳跃原理。
AI 中文摘要
本文在非更新驱动的二元风险模型中扩展了Yang和Li(2017)的结果。具体而言，我们关注具有两个任意相依计数过程的二元风险模型中，有限和无限时间范围内折现总索赔的联合尾部的渐近行为。我们进一步假设两个业务线的索赔额序列是独立的，但每条序列内部包含弱相依项。在我们的主要结果中，在有限和无限时间范围内，我们对计数过程假设了两个（不同的）一般条件，这些条件被除更新过程之外的广泛过程所满足。在有限时间范围内，我们假设两条业务线的索赔分布属于次指数分布类，而在无限时间范围内，我们限制在一致变化和正递减分布类。当索赔分布限制在正则变化类时，我们推导出更显式的渐近表达式。我们注意到，我们的结果表明折现总索赔存在多元非线性单大跳跃原理。
英文摘要
In this paper we extend the results from Yang and Li(2017), in a non-renewal driven bivariate risk model. Concretely, we are interested in the asymptotic behavior of the joint tail of the discounted aggregate claims over finite and infinite time horizon in a bivariate risk model with two arbitrarily dependent counting processes. We additionally suppose that the sequences of claim-sizes of the two lines of business are independent, but each of them contains weakly dependent terms. In our main results, on finite and on infinite time horizon, we assume two (different) general conditions for the counting processes, that are satisfied by a wide spectrum of processes beyond the renewal ones. In the case of finite horizon we suppose that the claim distributions from the two lines, belong to the subexponential distribution class, while in the case of infinite horizon we restrict ourselves to the consistently varying and positively decreasing distribution class. More explicit asymptotic expressions are derived in the case we are restricted on the regularly varying class for the claim distributions. We note that our results indicate the presence of multivariate non-linear single big jump principle for the discounted aggregate claims.
