Pricing ultra-long-dated pension liabilities under the market-consistent valuation is challenged by the scarcity of the long-term market instruments that match or exceed the terms of pension liabilities. We develop a robust self-financing hedging strategy which adopts a min–max expected shortfall hedging criterion to replicate the long-dated liabilities for agents who fear parameter misspecification. We introduce a backward robust least squares Monte Carlo method to solve this dynamic robust optimization problem. We find that both naive and robust optimal portfolios depend on the hedging horizon and the current funding ratio. The robust policy suggests taking more risk when the current funding ratio is low. The yield curve constructed by the robust dynamic hedging portfolio is always lower than the naive one but is higher than the model-based yield curve in a low-rate environment.

在市场一致的估值下对超长期养老金负债进行定价面临的挑战是，长期的市场工具缺乏匹配或超过养老金负债条款的稀缺性。我们开发了一种强大的自筹资金对冲策略，该策略采用了最小-最大预期缺口对冲标准来为担心参数错误指定的代理商复制长期负债。我们引入后向鲁棒最小二乘蒙特卡罗方法来解决此动态鲁棒优化问题。我们发现，天真和强大的最优投资组合都取决于对冲范围和当前的资金比率。强有力的政策建议在当前融资比例较低的情况下承担更多风险。