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

Abstract

This paper investigates the Parisian ruin probability for processes with power-asymmetric behavior of the variance near the unique optimal point. We derive the exact asymptotics as the ruin boundary tends to infinity and extend the previous result [1] to the case when the length of Parisian interval is of Pickands scale.As a primary application, we extend the recent result [2] on the many inputs proportional reinsurance fractional Brownian motion risk model to the Parisian ruin.