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.

中文翻译：

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资产负债管理的最坏情况条件风险价值：一般损失函数的框架


由于未来资产回报、员工工资和利率的不确定性，资产负债管理（ALM）是养老基金面临的一项具有挑战性的任务。为了应对这一挑战，本文提出了一种新的数学模型，该模型使用最坏情况条件风险价值（WCVaR）约束，以确保在最坏情况下，融资比率很有可能保持在监管机构规定的阈值之上。合理地解释历史样本数据的案例密度函数。该 WCVaR 约束的易于处理的重新表述是基于一般损失函数的最坏情况下偏矩 (WLPM) 的定义而开发的。此外，还构建了数据驱动的基于矩的模糊度集，以捕获 ALM 问题中随机变量的密度函数矩的不确定性。使用加拿大养老金计划 (CPP) 的真实世界数据对所提出的方法进行了评估，结果表明，在样本外数据上，该方法优于基于 CVaR 或具有固定矩的 WCVaR 的经典 ALM 模型。所提出的使用具有非线性损失函数的 WCVaR 处理相关不确定性的框架可用于其他应用领域。