Abstract
This article investigates the Parisian ruin probability for a class of Gaussian processes with power-asymmetric behavior of the variance near the unique optimal point. We derive the exact asymptotics as the initial capital tends to infinity and extend the previous result[8] to the case when the length of the Parisian interval is on the Pickands scale. As a primary application, we extend the recent result[13] on the many inputs proportional reinsurance fractional Brownian motion risk model to the Parisian ruin.
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