Ruin probabilities for two collaborating insurance companies

Zbigniew Michna

Papers from arXiv.org

Abstract: In this note we find a formula for the supremum distribution of spectrally positive or negative L\'evy processes with a broken linear drift. This gives formulas for ruin probabilities in the case when two insurance companies (or two branches of the same company) divide between them both claims and premia in some specified proportions. As an example we consider gamma L\'evy process, $\alpha$-stable L\'evy process and Brownian motion. Moreover we obtain identities for Laplace transform of the distribution for the supremum of L\'evy processes with randomly broken drift and on random intervals.

Date: 2018-04, Revised 2018-12
New Economics Papers: this item is included in nep-ias and nep-rmg
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