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Teoriya Veroyatnostei i ee Primeneniya, 2025, Volume 70, Issue 1, Pages 45–72
DOI: https://doi.org/10.4213/tvp5617 (Mi tvp5617) 		 
Two-dimensional Parisian ruin problem and computation of corresponding Pickands constants

G. A. Jasnovidova, A. A. Shemendyukb

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
b Department of Operations, Faculty of Business and Economics, University of Lausanne, Lausanne, Switzerland
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DOI: https://doi.org/10.4213/tvp5617
Abstract: We study the asymptotics of the simultaneous Parisian ruin problem of a two-\linebreak dimensional risk process defined by a fractional Brownian motion. This risk process models the profit process of insurance and reinsurance companies, where their insurance payments are shared in given proportions between the companies. We also propose a method for modeling Pickands and Piterbarg type constants, which appear in the asymptotics of the ruin probability under consideration.
Keywords: fractional Brownian motion, simultaneous Parisian ruin probability, Pickands and Piterbarg constants.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2022-289
Received: 30.11.2022
Revised: 09.09.2024
Accepted: 07.11.2024
Published: 27.01.2025
English version:
Theory of Probability and its Applications, 2025, Volume 70, Issue 1, Pages 37–59
DOI: https://doi.org/10.1137/S0040585X97T992227
Bibliographic databases:
Document Type: Article
MSC: Primary 60G15; secondary 60G70
Language: Russian
Citation: G. A. Jasnovidov, A. A. Shemendyuk, “Two-dimensional Parisian ruin problem and computation of corresponding Pickands constants”, Teor. Veroyatnost. i Primenen., 70:1 (2025), 45–72; Theory Probab. Appl., 70:1 (2025), 37–59
Citation in format AMSBIB
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\by G.~A.~Jasnovidov, A.~A.~Shemendyuk
\paper Two-dimensional Parisian ruin problem and computation of corresponding Pickands constants
\jour Teor. Veroyatnost. i Primenen.
\yr 2025
\vol 70
\issue 1
\pages 45--72
\mathnet{http://mi.mathnet.ru/tvp5617}
\crossref{https://doi.org/10.4213/tvp5617}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=4915318}
\transl
\jour Theory Probab. Appl.
\yr 2025
\vol 70
\issue 1
\pages 37--59
\crossref{https://doi.org/10.1137/S0040585X97T992227}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-105005887833}
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