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

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.