Second order asymptotics of aggregated log-elliptical risk

TL;DR

This paper derives the second order asymptotic approximation for the tail probability of sums of log-elliptical risks, improving accuracy over first order methods, with applications in finance and insurance.

Contribution

It introduces a second order asymptotic approximation for tail probabilities of log-elliptical risks, extending extreme value theory methods.

Findings

Second order approximation significantly improves over first order.

Applicable to log-normal risks in finance and insurance.

Numerical examples demonstrate enhanced accuracy.

Abstract

In this paper we establish the error rate of first order asymptotic approximation for the tail probability of sums of log-elliptical risks. Our approach is motivated by extreme value theory which allows us to impose only some weak asymptotic conditions satisfied in particular by log-normal risks. Given the wide range of applications of the log-normal model in finance and insurance our result is of interest for both rare-event simulations and numerical calculations. We present numerical examples which illustrate that the second order approximation derived in this paper significantly improves over the first order approximation.