An application of fractional differential equations to risk theory

By Corina Constantinescu, Jorge M. Ramírez, Wei Zhu. Finance and Stochastics, 2019

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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 size distributions exhibit rational Laplace transforms.

Subfields: Finance, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/772c2d5209d0b4387d1beda9ad8fbcf98ad563aa