Robust risk aggregation with neural networks.

Area of Science:

• Probability Theory
• Mathematical Finance
• Machine Learning

Background:

• Ambiguity in multivariate random variable distributions, particularly dependence structures, is common.
• Marginal distributions are known, but the joint distribution is uncertain, often requiring a reference measure.
• Risk aggregation involves quantifying the joint effect of multiple risks with known marginals but ambiguous interdependencies.

Purpose of the Study:

• To derive bounds for integrals over sets of distributions close to a reference measure while respecting marginal constraints.
• To develop a computationally feasible method for solving the derived dual problem in robust risk aggregation.
• To apply the proposed method to real-world risk aggregation scenarios.

Main Methods:

• Utilizing transportation distances (e.g., Wasserstein distance) to define distributional proximity.
• Deriving a dual representation of the bounding problem and proving strong duality.
• Employing neural networks for the numerical solution of the dual problem.

Main Results:

• A strong duality result is established for the problem of bounding integrals under distributional ambiguity.
• A practical and efficient neural network-based approach is presented for solving the dual problem.
• The method is validated on examples and successfully applied to robust risk aggregation.

Conclusions:

• The proposed framework effectively handles ambiguity in dependence structures for risk aggregation.
• Neural networks offer a powerful tool for robustly quantifying aggregated risks.
• The approach provides a computationally feasible solution for real-world risk management challenges.