Worst-case Conditional Value at Risk for asset liability management: A framework for general loss functions

Asset–liability management (ALM) is a challenging task faced by pension funds due to the uncertain nature of future asset returns, employees’ wages, and interest rates. To address this challenge, this paper presents a new mathematical model that uses a Worst-case Conditional Value-at-Risk (WCVaR) constraint to ensure that, with high probability, the funding ratio remains above a regulator-mandated threshold under the worst-case density function that plausibly explains historical sample data. A tractable reformulation of this WCVaR constraint is developed based on the definition of the Worst-case Lower Partial Moment (WLPM) for a general loss function. Additionally, a data-driven moment-based ambiguity set is constructed to capture uncertainty in the moments of the density functions of random variables in the ALM problem. The proposed approach is evaluated using real-world data from the Canada Pension Plan (CPP) and is shown to outperform classical ALM models, based on either CVaR or WCVaR with fixed moments, on out-of-sample data. The proposed framework for handling correlated uncertainty using WCVaR with nonlinear loss functions can be used in other application areas.