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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 Creative Commons