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Perturbation analysis of sub/super hedging problems
Author(s) -
Badikov Sergey,
Davis Mark H.A.,
Jacquier Antoine
Publication year - 2021
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/mafi.12321
Subject(s) - arbitrage , perturbation (astronomy) , duality (order theory) , extrapolation , mathematical economics , volatility (finance) , mathematical optimization , mathematics , economics , econometrics , financial economics , pure mathematics , mathematical analysis , physics , quantum mechanics
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 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.