Empirical regression quantile process with possible application to risk analysis

TL;DR

This paper introduces empirical regression quantile processes as tools for risk assessment in regression models, especially when covariates are uncontrollable, with applications in finance and environmental risk analysis.

Contribution

It develops empirical regression quantile processes and demonstrates their usefulness in probabilistic risk assessment across various fields.

Findings

Enables evaluation of expected α-shortfall and other risk measures.

Provides methods for risk measurement with uncontrolled covariates.

Applicable to financial and environmental risk analysis.

Abstract

The processes of the averaged regression quantiles and of their modifications provide useful tools in the regression models when the covariates are not fully under our control. As an application we mention the probabilistic risk assessment in the situation when the return depends on some exogenous variables. The processes enable to evaluate the expected $\alpha$-shortfall ($0\leq\alpha\leq 1$) and other measures of the risk, recently generally accepted in the financial literature, but also help to measure the risk in environment analysis and elsewhere.