Consider a multidimensional risk model, in which an insurer simultaneously confronts m (m ≥ 2) types of claims sharing a common non-stationary and non-renewal arrival process. Assuming that the claims arrival process satisfies a large deviation principle and the claim-size distributions are heavy-tailed, asymptotic estimates for two common types of ruin probabilities for this multidimensional risk model are obtained. As applications, we give two examples of the non-stationary point process: a Hawkes process and a Cox process with shot noise intensity, and asymptotic ruin probabilities are obtained for these two examples.

中文翻译：

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具有非平稳到达和次指数索赔的多维风险模型的破坏概率

考虑一个多维风险模型，其中保险公司同时面对m ( m ≥ 2) 种类型的索赔，这些索赔共享一个共同的非平稳和非更新到达过程。假设索赔到达过程满足大偏差原则并且索赔规模分布是重尾的，则获得了该多维风险模型的两种常见破产概率的渐近估计。作为应用，我们给出了两个非平稳点过程的例子：Hawkes 过程和具有散粒噪声强度的 Cox 过程，并获得了这两个例子的渐近毁灭概率。