The first passage event for sums of dependent L\'evy processes with applications to insurance risk

Irmingard Eder and Claudia Kl\"uppelberg

Papers from arXiv.org

Abstract: For the sum process $X=X^1+X^2$ of a bivariate L\'evy process $(X^1,X^2)$ with possibly dependent components, we derive a quintuple law describing the first upwards passage event of $X$ over a fixed barrier, caused by a jump, by the joint distribution of five quantities: the time relative to the time of the previous maximum, the time of the previous maximum, the overshoot, the undershoot and the undershoot of the previous maximum. The dependence between the jumps of $X^1$ and $X^2$ is modeled by a L\'evy copula. We calculate these quantities for some examples, where we pay particular attention to the influence of the dependence structure. We apply our findings to the ruin event of an insurance risk process.

Date: 2009-12
New Economics Papers: this item is included in nep-ecm and nep-ias
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Citations: View citations in EconPapers (4)

Published in Annals of Applied Probability 2009, Vol. 19, No. 6, 2047-2079

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:0912.1925

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