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

TL;DR

This paper addresses robustness in pension fund ALM under distributional uncertainty by comparing three DRO formulations—mixture, box, and Wasserstein ambiguity sets—against stochastic programming, using Canada Pension Plan data. The authors formulate a DRO ALM model with ambiguity sets for discount rates and asset returns, derive tractable reformulations for each set, and evaluate them via CPP-based scenario data generated with Monte Carlo GBM. Results show that Wasserstein and box DROs yield superior funding ratios and fund returns compared with mixture DRO and SP, with Wasserstein offering the strongest overall performance and diversification. The study demonstrates the value of distributional robustness for pension fund management and suggests extending the framework to other risk measures and distance metrics across different funds.

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.

Figures (4)

• Figure 1: Comparision of optimal asset allocation
• Figure 2: Optimal contribution rate for targeted funding ratios
• Figure 3: Funding Ratio of Different Models
• Figure 4: Fund Return of Different Models