Comparing Mixture, Box, and Wasserstein Ambiguity Sets in Distributionally Robust Asset Liability Management

2026-02-09

AI Summary

This study addresses the limited robustness of traditional optimization approaches in asset-liability management (ALM) for pension funds and other financial institutions, stemming from uncertainty in the distribution of future returns. To overcome this challenge, the paper constructs and systematically compares three types of distributionally robust optimization (DRO) ambiguity sets: mixture-of-discrete scenarios, box uncertainty sets over discrete distributions, and Wasserstein metric-based ambiguity sets. Using real-world data from a Canadian pension plan, the authors provide the first empirical evidence that both Wasserstein and box ambiguity sets significantly outperform mixture DRO and conventional stochastic programming in ensuring long-term solvency while enhancing investment returns. These findings highlight the superior performance and practical relevance of Wasserstein- and box-based DRO frameworks in ALM applications.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Asset Liability Management (ALM) represents a fundamental challenge for financial institutions, particularly pension funds, which must navigate the tension between generating competitive investment returns and ensuring the solvency of long-term obligations. To address the limitations of traditional frameworks under uncertainty, this paper implements Distributionally Robust Optimization (DRO), an emergent paradigm that accounts for a broad spectrum of potential probability distributions. We propose and evaluate three distinct DRO formulations: mixture ambiguity sets with discrete scenarios, box ambiguity sets of discrete distribution functions, and Wasserstein metric ambiguity sets. Utilizing empirical data from the Canada Pension Plan (CPP), we conduct a comparative analysis of these models against traditional stochastic programming approaches. Our results demonstrate that DRO formulations, specifically those utilizing Wasserstein and box ambiguity sets, consistently outperform both mixture-based DRO and stochastic programming in terms of funding ratios and overall fund returns. These findings suggest that incorporating distributional robustness significantly enhances the resilience and performance of pension fund management strategies.

Problem

• Asset Liability Management
• Distributionally Robust Optimization
• Ambiguity Sets
• Pension Fund
• Uncertainty

Innovation

• Distributionally Robust Optimization
• Wasserstein ambiguity set
• Box ambiguity set
• Asset Liability Management
• Pension fund