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An application of fractional differential equations to risk theory
Finance and Stochastics ( IF 1.7 ) Pub Date : 2019-07-12 , DOI: 10.1007/s00780-019-00400-8
Corina D. Constantinescu , Jorge M. Ramirez , Wei R. Zhu

This paper defines a new class of fractional differential operators alongside a family of random variables whose density functions solve fractional differential equations equipped with these operators. These equations can be further used to construct fractional integro-differential equations for the ruin probabilities in collective renewal risk models, with inter-arrival time distributions from the aforementioned family. Gamma-time risk models and fractional Poisson risk models are two specific cases among them, whose ruin probabilities have explicit solutions when claim size distributions exhibit rational Laplace transforms.

中文翻译:

分数阶微分方程在风险理论中的应用

本文定义了一类新的分数阶微分算子以及一系列随机变量,这些变量的密度函数可解决配备这些算子的分数阶微分方程。这些方程式可以进一步用于构建集体更新风险模型中毁灭概率的分数积分-微分方程式,以及上述族的到达时间间隔。伽马时间风险模型和分数泊松风险模型是其中的两个特定情况,当索赔大小分布显示有理Laplace变换时,其破产概率具有明确的解决方案。
更新日期:2019-07-12
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