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An Application of Fractional Differential Equations to Risk Theory

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 نشر من قبل Jorge Ramirez
 تاريخ النشر 2019
  مجال البحث
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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 sizes distributions exhibit rational Laplace transforms.



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