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On series expansions for scale functions and other ruin-related quantities
Scandinavian Actuarial Journal ( IF 1.8 ) Pub Date : 2019-09-13 , DOI: 10.1080/03461238.2019.1663444
David Landriault 1 , Gordon E. Willmot 1
Affiliation  

ABSTRACT In this note, we consider a nonstandard analytic approach to the examination of scale functions in some special cases of spectrally negative Lévy processes. In particular, we consider the compound Poisson risk process with or without perturbation from an independent Brownian motion. New explicit expressions for the first and second scale functions are derived which complement existing results in the literature. We specifically consider cases where the claim size distribution is gamma, uniform or inverse Gaussian. Some ruin-related quantities will also be re-examined in light of the aforementioned results.

中文翻译:

关于尺度函数和其他与废墟相关的量的级数展开

摘要 在本说明中,我们考虑了一种非标准分析方法,用于检查谱负列维过程的某些特殊情况下的尺度函数。特别是,我们考虑了有或没有来自独立布朗运动的扰动的复合泊松风险过程。导出了第一和第二尺度函数的新显式表达式,它们补充了文献中的现有结果。我们特别考虑索赔规模分布是伽马分布、均匀分布或逆高斯分布的情况。根据上述结果,一些与废墟相关的数量也将被重新检查。
更新日期:2019-09-13
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