Two-dimensional Parisian ruin problem and computation of corresponding Pickands constants

G. A. Jasnovidov^a, A. A. Shemendyuk<sup>b

a</sup> 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

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.

MSC: Primary 60G15; secondary 60G70

Received: 30.11.2022
Revised: 09.09.2024
Accepted: 07.11.2024

DOI: 10.4213/tvp5617

 English version: Theory of Probability and its Applications, 2025, 70:1, 37–59

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