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Perturbation analysis of sub/super hedging problems
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Title: | Perturbation analysis of sub/super hedging problems |
Authors: | Jacquier, A Badikov, S Davis, M |
Item Type: | Journal Article |
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 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. |
Issue Date: | 1-Oct-2021 |
Date of Acceptance: | 23-May-2021 |
URI: | http://hdl.handle.net/10044/1/89860 |
DOI: | 10.1111/mafi.12321 |
ISSN: | 0960-1627 |
Publisher: | Wiley |
Start Page: | 1240 |
End Page: | 1274 |
Journal / Book Title: | Mathematical Finance |
Volume: | 31 |
Issue: | 444 |
Copyright Statement: | © 2021 The Authors. Mathematical Finance published by Wiley Periodicals LLC This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. |
Keywords: | Social Sciences Science & Technology Physical Sciences Business, Finance Economics Mathematics, Interdisciplinary Applications Social Sciences, Mathematical Methods Business & Economics Mathematics Mathematical Methods In Social Sciences duality infinite-dimensional linear programing perturbation methods super-hedging ARBITRAGE BOUNDS VOLATILITY SMILE DUALITY PRICES q-fin.MF q-fin.MF math.PR 90C05, 90C46, 91G20, 46N10 Finance 0102 Applied Mathematics 1502 Banking, Finance and Investment |
Publication Status: | Published |
Online Publication Date: | 2021-06-11 |
Appears in Collections: | Financial Mathematics Faculty of Natural Sciences Mathematics |
This item is licensed under a Creative Commons License