Ruin Probabilities for Two Collaborating Insurance Companies

• Autorzy: Michna Zbigniew

Identyfikatory

DOI

10.37190/0208-4147.40.2.10

• Języki publikacji: EN

Abstrakty

EN

We find a formula for the supremum distribution of spectrally positive or negative Lévy processes with a broken linear drift. This gives formulas for ruin probabilities if two insurance companies (or two branches of the same company) divide between them both claims and premia in some specified proportions or if the premium rate for a given insurance portfolio is changed at a certain time. As an example we consider a gamma Lévy process, an -stable Lévy process and Brownian motion. Moreover we obtain identities for the Laplace transform of the distribution of the supremum of Lévy processes with a randomly broken drift (random time of the premium rate change) and on random intervals (random time when the insurance portfolio is closed).

Słowa kluczowe

EN

Lévy process; distribution of supremum stochastic process; ruin probability; gamma Lévy process; Lévy process α-stable

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2020
• Tom: Vol. 40, Fasc. 2
• Strony: 360--386
• Opis fizyczny: Bibliogr. 25 poz.

Twórcy

autor

Michna Zbigniew

• Department of Logistics, Wrocław University of Economics and Business, 53-345 Wrocław, Poland

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).