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A Note on Utility Maximization with Unbounded Random Endowment

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  • Keita Owari

Abstract

This paper addresses the applicability of the convex duality method for utility maximization, in the presence of random endowment. When the price process is a locally bounded semimartingale, we show that the fundamental duality relation holds true, for a wide class of utility functions and unbounded random endowments. We show this duality by exploiting Rockafellar's theorem on integral functionals, to a random utility function.

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File URL: http://gcoe.ier.hit-u.ac.jp/research/discussion/2008/pdf/gd09-091.pdf
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Bibliographic Info

Paper provided by Institute of Economic Research, Hitotsubashi University in its series Global COE Hi-Stat Discussion Paper Series with number gd09-091.

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Date of creation: Oct 2009
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Handle: RePEc:hst:ghsdps:gd09-091

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Keywords: Utility maximization; Convex duality method; Martingale measures;

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  1. Becherer, Dirk, 2003. "Rational hedging and valuation of integrated risks under constant absolute risk aversion," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 1-28, August.
  2. Hua He and Neil D. Pearson., 1989. "Consumption and Portfolio Policies with Incomplete Markets and Short-Sale Constraints: The Finite Dimensional Case," Research Program in Finance Working Papers RPF-189, University of California at Berkeley.
  3. Mark P. Owen & Gordan Žitković, 2009. "Optimal Investment With An Unbounded Random Endowment And Utility-Based Pricing," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 129-159.
  4. (**), Hui Wang & Jaksa Cvitanic & (*), Walter Schachermayer, 2001. "Utility maximization in incomplete markets with random endowment," Finance and Stochastics, Springer, vol. 5(2), pages 259-272.
  5. Owari, Keita, 2008. "Robust Exponential Hedging and Indifference Valuation," Discussion Papers 2008-09, Graduate School of Economics, Hitotsubashi University.
  6. Julien Hugonnier & Dmitry Kramkov & Walter Schachermayer, 2005. "On Utility-Based Pricing Of Contingent Claims In Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 15(2), pages 203-212.
  7. Yuri M. Kabanov & Christophe Stricker, 2002. "On the optimal portfolio for the exponential utility maximization: remarks to the six-author paper," Mathematical Finance, Wiley Blackwell, vol. 12(2), pages 125-134.
  8. Julien Hugonnier & Dmitry Kramkov, 2004. "Optimal investment with random endowments in incomplete markets," Papers math/0405293, arXiv.org.
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Cited by:
  1. Keita Owari, 2013. "A Robust Version of Convex Integral Functionals," CARF F-Series CARF-F-319, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  2. Keita Owari, 2011. "ON ADMISSIBLE STRATEGIES IN ROBUST UTILITY MAXIMIZATION (Forthcoming in "Mathematics and Financial Economics")," CARF F-Series CARF-F-257, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  3. Keita Owari, 2011. "On Admissible Strategies in Robust Utility Maximization," Papers 1109.5512, arXiv.org, revised Mar 2012.

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