Ruin probabilities in tough times - Part 1 - Heavy-traffic approximation for fractionally integrated random walks in the domain of attraction of a nonGaussian stable distribution

TL;DR

This paper develops heavy-traffic limit theorems for fractionally integrated random walks and FARIMA processes with stable distribution innovations, relevant to insurance mathematics and risk modeling.

Contribution

It introduces new heavy-traffic approximations for processes with non-Gaussian stable innovations, extending existing models to more realistic heavy-tailed scenarios.

Findings

Derived heavy-traffic limit theorems for fractional processes

Extended results to FARIMA processes with stable innovations

Applicable to insurance risk modeling with heavy-tailed data

Abstract

Motivated by applications to insurance mathematics, we prove some heavy-traffic limit theorems for process which encompass the fractionally integrated random walk as well as some FARIMA processes, when the innovations are in the domain of attraction of a nonGaussian stable distribution.