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Utility maximization in incomplete markets with random endowment

An Erratum to this article was published on 07 June 2017

Abstract.

This paper solves the following problem of mathematical finance: to find a solution to the problem of maximizing utility from terminal wealth of an agent with a random endowment process, in the general, semimartingale model for incomplete markets, and to characterize it via the associated dual problem. We show that this is possible if the dual problem and its domain are carefully defined. More precisely, we show that the optimal terminal wealth is equal to the inverse of marginal utility evaluated at the solution to the dual problem, which is in the form of the regular part of an element of \(({\bf L}^\infty)^*\) (the dual space of \({\bf L}^\infty\)).

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Manuscript received: November 1999; final version received: February 2000

An erratum to this article is available at http://dx.doi.org/10.1007/s00780-017-0331-9.

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Cvitanić, J., Schachermayer, W. & Wang, H. Utility maximization in incomplete markets with random endowment. Finance Stochast 5, 259–272 (2001). https://doi.org/10.1007/PL00013534

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  • DOI: https://doi.org/10.1007/PL00013534

  • Key words: Utility maximization, incomplete markets, random endowment, duality
  • JEL Classification: G11, G12; C61
  • Mathematics Subject Classification (1991): Primary 90A09, 90A10; secondary 90C26