engleski

Distribution of suprema for generalized risk processes

We study a generalized risk process X(t)=Y(t)−C(t), t∈[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 Xˆ=−X on [0, τ] which generalizes previously known results. We also discuss which assumptions are necessary for deriving this formula, especially from the point of view of the ladder process.

Ladder height process, Lévy process, modified ladder heights, net profit condition, Pollaczek–Khinchine formula, risk theory, subordinator, supremum, fluctuation theory

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