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This paper investigates the Parisian ruin probability for processes withpower-asymmetric behavior of the variance near the unique optimal point. Wederive the exact asymptotics as the ruin boundary tends to infinity and extendthe previous result arXiv:1504.07061 to the case when the length of Parisianinterval is of Pickands scale. As a primary application, we extend the recentresult arXiv:2010.00222 on the many inputs proportional reinsurance fractionalBrownian motion risk model to the Parisian ruin.

Parisian ruin with power-asymmetric variance near the optimal point with application to many-inputs proportional reinsurance