Abstract
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.
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.
| Original language | English |
|---|---|
| Pages (from-to) | 1001-1024 |
| Number of pages | 24 |
| Journal | Finance and Stochastics |
| Volume | 23 |
| Early online date | 12-Jul-2019 |
| DOIs | |
| Publication status | Published - Oct-2019 |
| Externally published | Yes |
Keywords
- Ruin probability
- Fractional differential operator
- Collective risk model