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A Note on Utility Maximization with Unbounded Random Endowment


This paper addresses the applicability of the convex duality method for utility maximization, in the presence of random endowment. When the underlying 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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Correspondence to Keita Owari.

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Owari, K. A Note on Utility Maximization with Unbounded Random Endowment. Asia-Pac Financ Markets 18, 89–103 (2011).

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  • Utility maximization
  • Convex duality method
  • Martingale measures