DO ARBITRAGE‐FREE PRICES COME FROM UTILITY MAXIMIZATION?. (20th May 2014)

• Record Type: Journal Article
• Authors: Siorpaes, Pietro
• Is Part Of: Mathematical finance. Volume 26:Number 3(2016:Jul.)
• Page Start: 602
• Page End: 616
• Publication Date: 2014-05-20
• Subjects: utility‐based pricing -- arbitrage free -- convex duality -- incomplete markets; Business mathematics -- Periodicals; 332
• DOI: 10.1111/mafi.12066
• Languages: English
• ISSNs: 0960-1627

Abstract

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.