Model Risk Static-Hedging a Constrained Distributionally Robust Optimization approach

We investigate model risk and distributionally robust optimization (DRO) under marginal and martingale constraints. Building on our previous work, we address the previously open case of static hedging with second-period maturity vanilla options and hedging strategies involving a vanilla payoff. We also extend recent sensitivity results to settings where admissible models must satisfy a martingale coupling constraint. Our approach relies on a weak implicit function theorem argument to construct families of measures satisfying the prescribed constraints. We derive closed-form sensitivity formulas and characterize the corresponding hedging strategies when the underlying process is real-valued.