On partial stochastic comparisons based on tail values at risk

TL;DR

This paper introduces a new family of stochastic orders based on tail value at risk for comparing heavy-tailed distributions, focusing on large losses and partial risk assessments.

Contribution

It proposes a novel family of stochastic orders indexed by a confidence level, connecting them with classical risk criteria and applying them to real datasets.

Findings

New stochastic orders relate to tail value at risk

Connections established with classical risk measures

Applications demonstrated with real data

Abstract

In risk theory, financial asset returns often follow heavy-tailed distributions. Investors and risk managers used to compare risk measures as the value at risk or tail value at risk in order over the whole confidence levels to avoid the exposure to to large risks. In this paper we analyze the comparison between tail values at risk from a confidence level and beyond which is a reasonable criterion when we are focused on large losses or simply we cannot give a complete ordering over all the confidence levels. A family of stochastic orders indexed by $p_0\in(0,1)$ is proposed. We study their properties and connections with other classical criteria as the increasing convex and tail convex orders and we rank some parametrical families of distributions. Finally, two applications with real datasets are given as well.