We study a generalized risk process $X(t)=Y(t)-C(t)$, $t\in[0,τ]$, where $Y$ is a Lévy process, $C$ an independent subordinator and $τ$ 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 $[0,τ]$ 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.