Robust asset pricing and superhedging duality under model uncertainty with and without short-sale constraints

Wenqing Zhang and Shuzhen Yang

Papers from arXiv.org

Abstract: We study asset pricing and hedging under model uncertainty in discrete time and finite states. For the single-period model, we characterize no-arbitrage by the existence of strictly positive martingale measures without short-sale restrictions and strictly positive supermartingale measures under short-sale prohibitions. In the constrained setting, we further consider a family of probability measures and introduce weak and strong risk-neutral nonlinear expectations. Their existence provides a necessary condition and a sufficient condition for no-arbitrage, respectively. We extend these results to multi-period markets, derive risk-neutral prices for replicable claims, and establish superhedging duality over the complete martingale and supermartingale families. A numerical illustration calibrated to monthly S&P 500 returns implements the pricing and superhedging framework for synthetic put and call options. The optimal values of the primal and complete dual problems agree to numerical precision, as predicted by the superhedging duality theorems. The results further show that short-sale prohibitions substantially increase put superhedging costs, while call costs are unchanged.

Date: 2024-08, Revised 2026-09
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