Naslov
Ruin probability for discrete risk processes

Autori
Geček Tuđen, Ivana

Izvornik
Studia scientiarum mathematicarum Hungarica (0081-6906) 56 (2019), 4; 420-439

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Skip-free random walk ; ballot theorem ; Kemperman's formula ; level crossing ; ruin probability ; Pollaczek-Khinchine formula

Sažetak
We study the discrete time risk process modelled by the skip-free random walk and derive results connected to the ruin probability and crossing a fixed level for this type of process. We use the method relying on the classical ballot theorems to derive the results for crossing a fixed level and compare them to the results known for the continuous time version of the risk process. We generalize this model by adding a perturbation and, still relying on the skip-free structure of that process, we generalize the previous results on crossing the fixed level for the generalized discrete time risk process. We further derive the famous Pollaczek-Khinchine type formula for this generalized process, using the decomposition of the supremum of the dual process at some special instants of time.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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