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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.

Suggested Citation

  • Keita Owari, 2009. "A Note on Utility Maximization with Unbounded Random Endowment," Global COE Hi-Stat Discussion Paper Series gd09-091, Institute of Economic Research, Hitotsubashi University.
  • Handle: RePEc:hst:ghsdps:gd09-091
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    File URL: http://gcoe.ier.hit-u.ac.jp/research/discussion/2008/pdf/gd09-091.pdf
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    Keywords

    Utility maximization; Convex duality method; Martingale measures;

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