New stochastic comparisons based on tail values at risk

TL;DR

This paper introduces a new method for comparing claims in insurance using Tail Value at Risk, focusing on conditional claims in stop loss and deductible contracts, with theoretical properties and practical examples.

Contribution

It proposes a novel criterion for stochastic comparison based on Tail Value at Risk for claims with conditional structures, including preservation properties and sufficient conditions.

Findings

New comparison criterion based on Tail Value at Risk

Preservation properties of the proposed comparisons

Illustrative examples demonstrating usefulness

Abstract

In this paper we provide a new criterion for the comparison of claims, when we have conditional claims arising in stop loss contracts or contracts with franchise deductible. These stochastic comparisons are made on the basis of the Tail Value at Risk (also known as conditional tail expectation), just for a fixed level and beyond. In particular, we explain the interest of comparing these quantities, study some preservation properties and, in addition, we provide sufficient conditions for its study. Finally we illustrate its usefulness with some examples.