Naslov
Distribution of suprema for generalized risk processes

Autori
Geček Tuđen, Ivana

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Skup
9th international workshop on applied probability (IWAP2018)

Mjesto i datum
Budimpešta, Mađarska, 18.09.2018. - 21.09.2018

Vrsta sudjelovanja
Poster

Vrsta recenzije
Recenziran

Ključne riječi
generalized risk process, subordinator, exponential time, ladder process, net profit condition

Sažetak
The basic risk model, known as the Cramér-Lundberg model, has been revisited many times in the risk theory and generalized in a few ways. We study the generalized risk process X(t) = Y (t) - C(t), t in [0, T], where Y is a Lévy process, C is an independent subordinator and T an independent exponential time. This allows us to observe the process in the context of the fluctuation theory for the Lévy processes. In this surrounding, we derive a Pollaczek- Khinchine type formula for the supremum of the dual-process -X on [0 ; T ] which generalizes the previously known results. We also drop the standard assumptions on the finite expectations of the processes Y and C and the net profit condition and discuss which assumptions are necessary for deriving our results. In the end, we revisit and explain the assumptions and obtained results from the point of view of the ladder process.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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