### Abstract

Multivariate characteristics of risk processes are of high interest to academic actuaries. In such models, the probability of ruin is obtained not only by considering initial reserves u but also the severity of ruin y and the surplus before ruin x. This ruin probability can be expressed using an integral equation that can be efficiently solved using the Gaver-Stehfest method of inverting Laplace transforms. This approach can be considered to be an alternative to recursive methods previously used in actuarial literature. © 1999 Elsevier Science B.V.

Original language | English |
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Pages (from-to) | 133-142 |

Number of pages | 10 |

Journal | Insurance: Mathematics and Economics |

Volume | 25 |

Issue number | 2 |

Publication status | Published - 16 Nov 1999 |

### Keywords

- G22
- IM13
- IM20
- Integral equations
- Laplace transform
- Multivariate ultimate ruin probability
- Numerical methods

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## Cite this

Usábel, M. A. (1999). Calculating multivariate ruin probabilities via Gaver-Stehfest inversion technique.

*Insurance: Mathematics and Economics*,*25*(2), 133-142.