Extreme-case Range Value-at-Risk under Increasing Failure Rate

TL;DR

This paper investigates the behavior of extreme-case range Value-at-Risk under distributional ambiguity with increasing failure rate, providing new insights for risk management in finance and insurance.

Contribution

It characterizes the properties of extreme-case distributions with IFR constraints and applies these findings to risk measures like stop-loss and limited loss variables.

Findings

Characterized extreme-case distributions under IFR constraints.

Derived formulas for extreme-case range VaR under distributional ambiguity.

Applied results to practical risk measures in finance and insurance.

Abstract

The extreme cases of risk measures, when considered within the context of distributional ambiguity, provide significant guidance for practitioners specializing in risk management of quantitative finance and insurance. In contrast to the findings of preceding studies, we focus on the study of extreme-case risk measure under distributional ambiguity with the property of increasing failure rate (IFR). The extreme-case range Value-at-Risk under distributional uncertainty, consisting of given mean and/or variance of distributions with IFR, is provided. The specific characteristics of extreme-case distributions under these constraints have been characterized, a crucial step for numerical simulations. We then apply our main results to stop-loss and limited loss random variables under distributional uncertainty with IFR.