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A Note on Utility Maximization with Unbounded Random Endowment

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  • Keita Owari

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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://hdl.handle.net/10.1007/s10690-010-9122-4
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Bibliographic Info

Article provided by Springer in its journal Asia-Pacific Financial Markets.

Volume (Year): 18 (2011)
Issue (Month): 1 (March)
Pages: 89-103

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Handle: RePEc:kap:apfinm:v:18:y:2011:i:1:p:89-103

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Web page: http://springerlink.metapress.com/link.asp?id=102851

Related research

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

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References

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  1. 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.
  2. Hua He and Neil D. Pearson., 1989. "Consumption and Portfolio Policies with Incomplete Markets and Short-Sale Constraints: The Infinite Dimensional Case," Research Program in Finance Working Papers RPF-191, University of California at Berkeley.
  3. Julien Hugonnier & Dmitry Kramkov, 2004. "Optimal investment with random endowments in incomplete markets," Papers math/0405293, arXiv.org.
  4. 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.
  5. 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.
  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. (**), 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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Citations

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Cited by:
  1. 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.
  2. Keita Owari, 2011. "On Admissible Strategies in Robust Utility Maximization," Papers 1109.5512, arXiv.org, revised Mar 2012.

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