摘要翻译：
我们首先证明了在具有常利率力的经典风险模型中，有限时间绝对破产概率可以用正的Ornstein-Uhlenbeck型过程的转移概率表示，例如X。我们的方法适用于总索赔过程的动力学是从属的情况。从这个表达式，我们很容易地推导出无限时间绝对破产发生的充要条件。我们进一步证明，在某些技术条件下，X的跃迁密度允许一个谱型表示，只涉及过程的极限分布。作为副产品，我们得到了有限时间绝对破产概率的级数展开式。在此基础上，我们还导出了上述风险过程的第一次退出时间的拉普拉斯变换。最后，我们通过一些例子来说明我们的结果。
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英文标题：
《Absolute ruin in the Ornstein-Uhlenbeck type risk model》
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作者：
Ronnie L. Loeffen and Pierre Patie
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最新提交年份：
2010
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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英文摘要：
  We start by showing that the finite-time absolute ruin probability in the classical risk model with constant interest force can be expressed in terms of the transition probability of a positive Ornstein-Uhlenbeck type process, say X. Our methodology applies to the case when the dynamics of the aggregate claims process is a subordinator. From this expression, we easily deduce necessary and sufficient conditions for the infinite-time absolute ruin to occur. We proceed by showing that, under some technical conditions, the transition density of X admits a spectral type representation involving merely the limiting distribution of the process. As a by-product, we obtain a series expansions for the finite-time absolute ruin probability. On the way, we also derive, for the aforementioned risk process, the Laplace transform of the first-exit time from an interval from above. Finally, we illustrate our results by detailing some examples.
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PDF链接：
https://arxiv.org/pdf/1006.2712