非标准风险模型中局部一致渐近性及系统性因素引发的保险与金融风险交互作用

中文摘要 AI 辅助

本文研究了具有任意相依保险与金融风险的多变量风险模型中，折扣总索赔进入某些稀有集合的概率关于时间的局部一致渐近表达式。我们的模型基于Guo（2022）引入模型的多变量版本，并考虑保险公司投资组合的对数收益过程由跳跃扩散过程描述。保险与金融风险之间的相依性由索赔向量与收益跳跃之间的相依性所隐含，且在索赔向量和折扣索赔向量的某些分布条件下是任意的。与以往关于该主题的论文相反，除了多维扩展外，我们考虑模型由共同计数过程驱动，该过程不一定是更新过程，索赔向量是相互依存的，且其分布不限于（多变量）正则变化分布类。在索赔向量和折扣索赔向量服从多变量一致变化和正递减分布类的条件下，以及在跳跃和计数过程的某些矩条件下，我们的主要结果表明，在这个不一定是Levy-更新环境中，折扣总索赔存在多变量线性单大跳跃原理。在将分布限制为多变量正则变化后，我们在跳跃的稍弱矩条件下获得了更显式的表达式。我们提供了一个推论，其中在弱相依结构下满足主要结果的条件，并利用相依性求解技术找到了更显式的渐近表达式。

英文摘要

In this paper we study local uniform, with respect to time, asymptotic expressions for the asymptotic behavior of the entrance probability of discounted aggregate claims to some rare sets, in a multivariate risk model with arbitrarily dependent insurance and financial risks. Our model is based on a multivariate version of a model, introduced by Guo (2022), and we consider that the logarithmic return process of the insurers investment portfolio is described by a jump-diffusion process. The dependence between the insurance and financial risks is implied by the dependence of the claim-vectors with the jumps of returns, and is arbitrary under some distributional conditions on the claim-vectors and the discounted claim-vectors. In opposite to previous papers on this topic, except the multidimensional extension, we consider that the model is driven by a common counting process, that is not necessarily renewal, the claim vectors are interdependent, and their distribution is not restricted to the class of (multivariate) regularly varying distributions. Under the condition that the claim vectors, and the discounted claim-vectors follows distributions from the class of multivariate consistently varying and positively decreasing distributions, and under some moment conditions on the jumps and the counting process, our main result shows the presence of multivariate linear single big jump principle of the discounted aggregate claims in this not necessarily Levy-Renewal environment. After restriction of the distributions to multivariate regular variation, we obtain more explicit expressions, under a slightly weaker moment condition on the jumps. We provide a corollary, in which the conditions of the main result are satisfied under a weak dependence structure and we find a more explicit asymptotic expression, using the technique of solution of the dependence.

发表机构

• University of the Aegean（爱琴海大学）
• Dongbei University of Finance and Economy（东北财经大学）

机构由 AI 辅助整理，请以论文原文为准。