On suprema of Lévy processes and application in risk theory (Q731712)

The authors consider a general Lévy process \(Y\), an independent subordinator \(C\) and define the process \(X=Y-C\). They study the times when a new supremum of the process \(-X\) is reached by a jump of the subordinator \(C\). The main result gives a necessary and sufficient condition for such times to be discrete. The proof of a Pollaczek-Hinchin-type is sketched for the distribution of the supremum of the process \(-X\) in the case when \(X\) drifts to \(\infty\) and the times when a new supremum of \(-X\) is reached by a jump of the subordinator \(C\) are discrete.