A significant limitation of conventional risk theory models in insurance is the explicit assumption that different lines of insurance business operations are uncorrelated. This paper addresses this limitation by introducing a novel multivariate size-dependent renewal risk model. The authors adopt a t-copula-based approach to model dependence structures between different types of claims, allowing for a more flexible class of sub-exponential distributions. Furthermore, the model incorporates economic indicators, policyholder behavior, and external events, providing a comprehensive risk assessment. The findings include precise large deviation results for aggregate claims, highlighting the significant impact of complex dependencies on risk measures. Additionally, the authors develop a lemma and provide detailed proof, which is crucial for establishing the theoretical foundation of the results. The insights drawn from numerical simulations innovate the understanding of tail behavior in insurance risk models, with important implications for risk management and premium setting.

中文翻译：

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t-copula 依赖性更新风险模型中亚指数多变量和的精确大偏差


保险业传统风险理论模型的一个重大局限性是明确假设不同的保险业务运营线是不相关的。本文通过引入一种新的多变量大小依赖性更新风险模型来解决这一限制。作者采用基于 t-copula 的方法对不同类型权利要求之间的依赖关系结构进行建模，从而允许更灵活的子指数分布类别。此外，该模型还结合了经济指标、投保人行为和外部事件，提供了全面的风险评估。调查结果包括汇总索赔的精确大偏差结果，突出了复杂依赖关系对风险度量的重大影响。此外，作者开发了一个引理并提供了详细的证明，这对于建立结果的理论基础至关重要。从数值模拟中得出的见解创新了对保险风险模型中尾部行为的理解，对风险管理和保费设定具有重要意义。