离散时间风险模型中破产概率的近似

arXiv: Probability Pub Date : 2020-06-02 DOI:10.15559/20-vmsta158

David J. Santana, Luis Rincón

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引用次数: 6

摘要

基于离散版的Pollaczeck-Khinchine公式，给出了当索赔服从负二项混合分布时Gerber-Dickson风险模型中最终破产概率的一般计算方法。然后将结果推广到具有混合泊松分布的索赔。所得到的公式允许进行一些近似过程。给出了几个例子，并给出了数值证据，证明了近似的准确性。

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Approximations of the ruin probability in a discrete time risk model

Based on a discrete version of the Pollaczeck-Khinchine formula, a general method to calculate the ultimate ruin probability in the Gerber-Dickson risk model is provided when claims follow a negative binomial mixture distribution. The result is then extended for claims with a mixed Poisson distribution. The formula obtained allows for some approximation procedures. Several examples are provided along with the numerical evidence of the accuracy of the approximations.

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arXiv: Probability

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