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

TL;DR

This paper analyzes the Parisian ruin probability for processes with asymmetric variance behavior near an optimal point, deriving exact asymptotics and extending previous models to many-input reinsurance scenarios.

Contribution

It introduces new asymptotic results for Parisian ruin probabilities with power-asymmetric variance and extends reinsurance risk models to the Parisian setting.

Findings

Derived exact asymptotics for ruin probabilities

Extended previous models to many-input proportional reinsurance

Analyzed variance behavior near the optimal point

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 arXiv:1504.07061 to the case when the length of Parisian interval is of Pickands scale. As a primary application, we extend the recent result arXiv:2010.00222 on the many inputs proportional reinsurance fractional Brownian motion risk model to the Parisian ruin.