  In this contribution we study asymptotics of the simultaneous Parisian ruin
probability of a two-dimensional fractional Brownian motion risk process. This
risk process models the surplus processes of an insurance and a reinsurance
companies, where the net loss is distributed between them in given proportions.
We also propose an approach for simulation of Pickands and Piterbarg constants
appearing in the asymptotics of the ruin probability.
