Two-Dimensional Parisian Ruin Problem and Evaluation of Pickands Type Constants

We study the asymptotics of the simultaneous Parisian ruin problem of a two-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.