Do arbitrage-free prices come from utility maximization?

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Title: Do arbitrage-free prices come from utility maximization?
Author(s): Siorpaes, P
Item Type: Journal Article
Abstract: In this paper we ask whether, given a stock market and an illiquid derivative, there exists arbitrage-free prices at which a utility-maximizing agent would always want to buy the derivative, irrespectively of his own initial endowment of derivatives and cash. We prove that this is false for any given investor if one considers all initial endowments with finite utility, and that it can instead be true if one restricts to the endowments in the interior. We show, however, how the endowments on the boundary can give rise to very odd phenomena; for example, an investor with such an endowment would choose not to trade in the derivative even at prices arbitrarily close to some arbitrage price.
Publication Date: 20-May-2014
Date of Acceptance: 1-Dec-2013
URI: http://hdl.handle.net/10044/1/57656
DOI: https://dx.doi.org/10.1111/mafi.12066
ISSN: 0960-1627
Publisher: Wiley
Start Page: 602
End Page: 616
Journal / Book Title: Mathematical Finance
Volume: 26
Issue: 3
Copyright Statement: © 2014 Wiley Periodicals, Inc. This is the peer reviewed version of the article, which has been published in final form at https://dx.doi.org/10.1111/mafi.12066. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.
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
utility-based pricing
arbitrage free
convex duality
incomplete markets
INCOMPLETE MARKETS
OPTIMAL INVESTMENT
CONTINGENT CLAIMS
q-fin.PM
q-fin.PM
math.PR
91Gxx
Social Sciences
Science & Technology
Physical Sciences
Business, Finance
Economics
Mathematics, Interdisciplinary Applications
Social Sciences, Mathematical Methods
Business & Economics
Mathematics
Mathematical Methods In Social Sciences
utility-based pricing
arbitrage free
convex duality
incomplete markets
INCOMPLETE MARKETS
OPTIMAL INVESTMENT
CONTINGENT CLAIMS
0102 Applied Mathematics
1502 Banking, Finance And Investment
Finance
Publication Status: Published
Appears in Collections:Financial Mathematics
Mathematics
Faculty of Natural Sciences



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