Pareto models for risk management

TL;DR

This paper explores Pareto-type models that incorporate second order behavior to improve risk measure estimation in finance and insurance, extending traditional Pareto models for better practical fit.

Contribution

It introduces methods to transition from strict Pareto models to Pareto-type distributions, including inference techniques and formulas for risk measures.

Findings

Enhanced fit for tail distributions in risk management

Derived formulas for Value-at-Risk and Expected Shortfall

Applications demonstrated on insurance and financial data

Abstract

The Pareto model is very popular in risk management, since simple analytical formulas can be derived for financial downside risk measures (Value-at-Risk, Expected Shortfall) or reinsurance premiums and related quantities (Large Claim Index, Return Period). Nevertheless, in practice, distributions are (strictly) Pareto only in the tails, above (possible very) large threshold. Therefore, it could be interesting to take into account second order behavior to provide a better fit. In this article, we present how to go from a strict Pareto model to Pareto-type distributions. We discuss inference, and derive formulas for various measures and indices, and finally provide applications on insurance losses and financial risks.