Perturbation Analysis of Sub/Super Hedging Problems
29 Pages Posted: 28 Jun 2018
Date Written: June 12, 2018
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 abstract 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 finally perform a rigorous perturbation analysis of those linear programming problems, and highlight, as a numerical example, the influence of smile extrapolation on the bounds of exotic options.
Keywords: duality, infinity-dimensional linear programming, super-hedging, perturbation methods
JEL Classification: 90C05, 90C46, 91G20, 46N10
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