Naslov
On suprema of Levy processes and application in risk theory

Autori
Song, Renming ; Vondraček, Zoran

Izvornik
Annales de l institut henri poincare-probabilites et statistiques (0246-0203) 44 (2008), 5; 977-986

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

Ključne riječi
Levy process ; subordinator ; fluctuation theory ; extrema ; risk theory

Sažetak
Let $\wh{; ; ; ; X}; ; ; ; =C-Y$ where $Y$ is a general one-dimensional Levy process and $C$ an independent subordinator. Consider the times when a new supremum of $\wh{; ; ; ; X}; ; ; ; $ is reached by a jump of the subordinator $C$. We give a necessary and sufficient condition in order for such times to be discrete. When this is the case and $\wh{; ; ; ; X}; ; ; ; $ drifts to $-\infty$, we decompose the absolute supremum of $\wh{; ; ; ; X}; ; ; ; $ at these times, and derive a Pollaczek-Hinchin-type formula for the distribution function of the supremum.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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