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arXiv · 1704.07340

Distribution of suprema for generalized risk processes

Ivana Geček Tuđen
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Abstract

We study a generalized risk process $X(t)=Y(t)-C(t)$, $t\in[0,\tau]$, where $Y$ is a L\'evy process, $C$ an independent subordinator and $\tau$ an independent exponential time. Dropping the standard assumptions on the finite expectations of the processes $Y$ and $C$ and the net profit condition, we derive a Pollaczek-Khinchine type formula for the supremum of the dual process $\widehat{X}=-X$ on $[0,\tau]$ which generalizes the results obtained in \cite{HPSV1}. We also discuss which assumptions are necessary for deriving this formula, specially from the point of view of the ladder process.

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Ivana Geček Tuđen. 2017-04-24. Distribution of suprema for generalized risk processes. https://arxiv.org/abs/1704.07340

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