Procesy Lévy’ego w modelach ubezpieczeniowych
Lévy processes in insurance models
Author(s): Zbigniew MichnaSubject(s): Economy
Published by: Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu
Keywords: Lévy process; α-stable Lévy process; gamma process; finite time ruin probability; infinite time ruin probability; asymptotic behaviour of ruin probability; subordinated process; stochastic integral
Summary/Abstract: In this article we review the concept of Lévy processes in risk theory. We emphasize the risk model with gamma process analyzing ruin probability of gamma process. We give an asymptotic behaviour of ruin probabilities and exact formula for finite time ruin probability for gamma process. We also consider models described by the so-called subordinated Levy processes. As a theoretical generalization we investigate supremum distribution of certain stochastic integrals.
Journal: Prace Naukowe Uniwersytetu Ekonomicznego we Wrocławiu
- Issue Year: 2011
- Issue No: 207
- Page Range: 149-156
- Page Count: 8
- Language: Polish
