Perturbation analysis of sub/super hedging problems

We investigate the links between various no‐arbitrage conditions and the existence of pricing functionals in general markets, and prove the Fundamental Theorem of Asset Pricing therein. No‐arbitrage conditions, either in this setting or in the case of a market consisting of European Call options, give rise to duality properties of infinite‐dimensional sub‐ and super‐hedging problems. With a view towards applications, we show how duality is preserved when reducing these problems over finite‐dimensional bases. We also introduce a rigorous perturbation analysis of these linear programing problems, and highlight numerically the influence of smile extrapolation on the bounds of exotic options.