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Do arbitrage-free prices come from utility maximization?

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  • Pietro Siorpaes
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    Abstract

    In this paper we ask whether, given a stock market and an illiquid derivative, there exists arbitrage-free prices at which an 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.

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    File URL: http://arxiv.org/pdf/1207.4749
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1207.4749.

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    Date of creation: Jul 2012
    Date of revision: Oct 2013
    Handle: RePEc:arx:papers:1207.4749

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    Web page: http://arxiv.org/

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    Cited by:
    1. Pietro Siorpaes, 2012. "Optimal Investment with Stocks and Derivatives," Papers 1210.5466, arXiv.org, revised Oct 2013.

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