Perturbation analysis of sub/super hedging problems

DOI10.1111/MAFI.12321zbMATH Open1522.91259arXiv1806.03543OpenAlexW3171232851MaRDI QIDQ6054380

Sergey Badikov, Mark Davis, Antoine Jacquier

Publication date: 28 September 2023

Published in: Mathematical Finance (Search for Journal in Brave)

Abstract: 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 numerically the influence of smile extrapolation on the bounds of exotic options.

Full work available at URL: https://arxiv.org/abs/1806.03543

zbMATH Keywords

dualityperturbation methodssuper-hedginginfinite-dimensional linear programing

Mathematics Subject Classification ID

Linear programming (90C05) Derivative securities (option pricing, hedging, etc.) (91G20) Perturbations in context of PDEs (35B20)

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