Tail Asymptotics of Deflated Risks

TL;DR

This paper studies the detailed tail behavior of deflated risks, providing advanced approximations and estimations for risk measures like Value at Risk under second-order regular variation assumptions.

Contribution

It introduces second-order tail asymptotics for deflated risks and applies these results to risk measurement and tail probability estimation.

Findings

Derived second-order tail asymptotics for deflated risks

Provided improved approximations for Value at Risk

Analyzed tail behavior of aggregated deflated risks

Abstract

Random deflated risk models have been considered in recent literatures. In this paper, we investigate second-order tail behavior of the deflated risk X=RS under the assumptions of second-order regular variation on the survival functions of the risk R and the deflator S. Our findings are applied to approximation of Value at Risk, estimation of small tail probability under random deflation and tail asymptotics of aggregated deflated risk