Tail approximation for reinsurance portfolios of Gaussian-like risks

TL;DR

This paper analyzes the tail behavior of two reinsurance portfolios with Gaussian-like risks, establishing asymptotic properties, dependence structure, and relations between scaled and unscaled portfolios.

Contribution

It provides new asymptotic results for Gaussian-like risk portfolios and explores their dependence properties, which were not previously characterized.

Findings

Tail asymptotics of reinsurance portfolios are derived.

Gaussian-like risks exhibit asymptotic independence.

Weak tail dependence coefficient is non-negative.

Abstract

We consider two different portfolios of proportional reinsurance of the same pool of risks. This contribution is concerned with Gaussian-like risks, which means that for large values the survival function of such risks is, up to a multiplier, the same as that of a standard Gaussian risk. We establish the tail asymptotic behavior of the total loss of each of the reinsurance portfolios and determine also the relation between randomly scaled Gaussian-like portfolios and unscaled ones. Further we show that jointly two portfolios of Gaussian-like risks exhibit asymptotic independence and their weak tail dependence coefficient is non-negative.