Formula for the supremum distribution of a spectrally positive \(\alpha \)-stable Lévy process

DOI10.1016/J.SPL.2010.11.014zbMath1208.60043arXiv1104.1976OpenAlexW2069782247MaRDI QIDQ625005

Zbigniew Michna

Publication date: 11 February 2011

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1104.1976

zbMATH Keywords

\(\alpha\)-stable Lévy processfinite time ruin probabilitydistribution of the supremum of a stochastic process

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Extreme value theory; extremal stochastic processes (60G70) Stable stochastic processes (60G52)

Related Items (5)

The Class of Distributions Associated with the Generalized Pollaczek-Khinchine Formula ⋮ Ruin probabilities for two collaborating insurance companies ⋮ On the supremum of the spectrally negative stable process with drift ⋮ Finite-time survival probability and credit default swaps pricing under geometric Lévy markets ⋮ Short proofs in extrema of spectrally one sided Lévy processes

Uses Software

• STABLE

Cites Work

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• A note on the supremum of a stable process
• Numerical calculation of stable densities and distribution functions
• The numerical calculation ofU(w, t), the probability of non-ruin in an interval (0,t)

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