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On utility maximization in discrete-time financial market models

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  • Miklos Rasonyi
  • Lukasz Stettner
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    Abstract

    We consider a discrete-time financial market model with finite time horizon and give conditions which guarantee the existence of an optimal strategy for the problem of maximizing expected terminal utility. Equivalent martingale measures are constructed using optimal strategies.

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    File URL: http://arxiv.org/pdf/math/0505243
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number math/0505243.

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    Date of creation: May 2005
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    Publication status: Published in Annals of Applied Probability 2005, Vol. 15, No. 2, 1367-1395
    Handle: RePEc:arx:papers:math/0505243

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    Web page: http://arxiv.org/

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    References

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    1. Julien Hugonnier & Dmitry Kramkov & Walter Schachermayer, 2005. "On Utility-Based Pricing Of Contingent Claims In Incomplete Markets," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 15(2), pages 203-212.
    2. B. Bouchard & N. Touzi & A. Zeghal, 2004. "Dual formulation of the utility maximization problem: the case of nonsmooth utility," Papers math/0405290, arXiv.org.
    3. Elyégs Jouini & Hédi Kallal, 1995. "Arbitrage In Securities Markets With Short-Sales Constraints," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 5(3), pages 197-232.
    4. J. Jacod & A.N. Shiryaev, 1998. "Local martingales and the fundamental asset pricing theorems in the discrete-time case," Finance and Stochastics, Springer, Springer, vol. 2(3), pages 259-273.
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    Cited by:
    1. Miklós Rásonyi & Andrea Rodrigues, 2013. "Optimal portfolio choice for a behavioural investor in continuous-time markets," Annals of Finance, Springer, Springer, vol. 9(2), pages 291-318, May.
    2. Mikl\'os R\'asonyi & Jos\'e G. Rodr\'iguez-Villarreal, 2014. "Optimal investment under behavioural criteria -- a dual approach," Papers 1405.3812, arXiv.org, revised Jun 2014.
    3. Laurence Carassus & Miklós Rásonyi, 2011. "Risk-averse asymptotics for reservation prices," Annals of Finance, Springer, Springer, vol. 7(3), pages 375-387, August.
    4. Roman Muraviev, 2011. "Additive habits with power utility: Estimates, asymptotics and equilibrium," Papers 1108.2889, arXiv.org.

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