In this paper, we consider a nonstandard multidimensional risk model, in which the claim sizes $\{\vec{X}_k, k\ge 1\}$ form an independent and identically distributed random vector sequence with dependent components. By assuming that there exists the regression dependence structure between inter-arrival time and the claim-size vectors, we extend the regression dependence to a more practical multidimensional risk model. For the univariate marginal distributions of claim vectors with consistently varying tails, we obtain the precise large deviation formulas for the multidimensional risk model with the regression size-dependent structure.

中文翻译：

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具有回归依赖结构的多维风险模型的精确大偏差

在本文中，我们考虑一个非标准的多维风险模型，其中索赔规模 $\{\vec{X}_k, k\ge 1\}$ 形成具有相关分量的独立且同分布的随机向量序列。通过假设到达间隔时间和索赔大小向量之间存在回归依赖结构，我们将回归依赖扩展到更实用的多维风险模型。对于具有一致变化尾部的索赔向量的单变量边际分布，我们获得了具有回归大小相关结构的多维风险模型的精确大偏差公式。