Abstract
Due to the scarcity of long-term market instruments, valuation of an ultra long-term pension liability under the market-consistent valuation framework must be model based. We develop a robust self-financing hedging strategy which adopts a min-max expected shortfall hedging criterion to replicate the long dated liability for agents who fear model 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 to take more risk when the current funding ratio is low. The artificial yield curve constructed by the robust dynamic hedging portfolio is lower than the naive one but is higher than the model based yield curve in a low rate environment.