Ruin probabilities in tough times - Part 2 - Heavy-traffic approximation for fractionally differentiated random walks in the domain of attraction of a nonGaussian stable distribution

TL;DR

This paper develops heavy-traffic limit theorems for fractionally differentiated 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 domain of attraction, extending prior results to more complex dependent processes.

Findings

Established heavy-traffic limit theorems for fractional processes

Extended results to FARIMA processes with stable innovations

Provided theoretical foundations for risk modeling in insurance

Abstract

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