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A Note on Utility Maximization with Unbounded Random Endowment

  • Keita Owari

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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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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  1. Julien Hugonnier & Dmitry Kramkov, 2004. "Optimal investment with random endowments in incomplete markets," Papers math/0405293, arXiv.org.
  2. 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.
  3. Hua He & Neil D. Pearson, 1991. "Consumption and Portfolio Policies With Incomplete Markets and Short-Sale Constraints: the Finite-Dimensional Case," Mathematical Finance, Wiley Blackwell, vol. 1(3), pages 1-10.
  4. 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.
  5. 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.
  6. Keita Owari, 2010. "Robust Exponential Hedging And Indifference Valuation," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(07), pages 1075-1101.
  7. 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.
  8. (**), 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.
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