Naslov
Ruin probabilities for competing claim processes

Autori
Huzak, Miljenko ; Perman, Mihael ; Šikić, Hrvoje ; Vondraček, Zoran

Izvornik
Journal of applied probability (0021-9002) 41 (2004), 3; 679-690

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

Ključne riječi
Risk theory ; ruin probability ; Pollaczek-Hinchin formula ; subordinator ; spectrally negative Levy process

Sažetak
Let $C_1, C_2, \ldots, C_m$ be independent subordinators with finite expectations and denote their sum by $C$. Consider the classical risk process $X(t)=x+ct -C(t)$. The ruin probability is given by the well known Pollaczek-Hinchin formula. If ruin occurs, however, it will be caused by a jump of one of the subordinators whose sum constitutes $C$. Formulae for the probability that ruin is caused by $C_i$ are derived. These formulae can be extended to perturbed risk processes of the type $X(t)=x+ct-C(t)+Z(t)$ where $Z$ is a L\'evy process with mean 0 and no positive jumps.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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