SUPER-HEDGING AMERICAN OPTIONS WITH SEMI-STATIC TRADING STRATEGIES UNDER MODEL UNCERTAINTY

摘要

We consider the super-hedging price of an American option in a discrete-time market in which stocks are available for dynamic trading and European options are available for static trading. We show that the super-hedging price π is given by the supremum over the prices of the American option under randomized models. That is, π = sup_((c_i,Q_i)_i)∑_i c_iΦ~(Q_i), where c_i ∈ R_+ and the martingale measure Q~i are chosen such that Pi ci = 1 and Pi ciQi prices the European options correctly, and ΦQ~i is the price of the American option under the model Q_i. Our result generalizes the example given in Hobson & Neuberger (2016) that the highest model-based price can be considered as a randomization over models.