A General Duality Relation with Applications in Quantitative Risk Management

TL;DR

This paper introduces a general duality framework for risk aggregation in scenarios with limited data, unifying and extending existing models to improve robustness in risk management.

Contribution

It formulates a comprehensive duality relation that generalizes known models and applies to new risk management scenarios with minimal data.

Findings

Unified duality framework for risk aggregation

Extension of models to new risk management applications

Provides robust bounds under data scarcity

Abstract

A fundamental problem in risk management is the robust aggregation of different sources of risk in a situation where little or no data are available to infer information about their dependencies. A popular approach to solving this problem is to formulate an optimization problem under which one maximizes a risk measure over all multivariate distributions that are consistent with the available data. In several special cases of such models, there exist dual problems that are easier to solve or approximate, yielding robust bounds on the aggregated risk. In this chapter we formulate a general optimization problem, which can be seen as a doubly infinite linear programming problem, and we show that the associated dual generalizes several well known special cases and extends to new risk management models we propose.