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Analysis and Optimization of Systes pp 3–23Cite as

Optimality conditions for utility maximization in an incomplete market

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Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 144))

Abstract

The problem of maximizing expected utility of final wealth in an incomplete market is investigated. The incomplete market is modelled by a bond and a finite number of stocks, the latter being driven by a d-dimensional Brownian motion. The coefficients of the bond and stock price processes are adapted to this Brownian motion, and the number of stocks is less than or equal to the dimension of the driving Brownian motion. It is shown that there is a way to “fictitiously” complete this market so that the optimal protfolio for the resulting completed market coincides with the optimal portfolio for the original incomplete market. A number of equivalent characterizations of the fictitious completion are given, and examples are provided.

Research supported by the National Science Foundation under Grant DMS-87-23078.

Research supported by the National Science Foundation under Grant DMS-87-02537.

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Author information

Authors and Affiliations

  1. Columbia University, 10027, New York, NY

    Ioannis Karatzas

  2. Carnegie Mellon University, 15213, Pittsburgh, PA

    John P. Lehoczky, Steven E. Shreve & Gan-Lin Xu

Authors
  1. Ioannis Karatzas
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  2. John P. Lehoczky
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  3. Steven E. Shreve
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  4. Gan-Lin Xu
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Editor information

A. Bensoussan J. L. Lions

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© 1990 Springer-Verlag

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Karatzas, I., Lehoczky, J.P., Shreve, S.E., Xu, GL. (1990). Optimality conditions for utility maximization in an incomplete market. In: Bensoussan, A., Lions, J.L. (eds) Analysis and Optimization of Systes. Lecture Notes in Control and Information Sciences, vol 144. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0120024

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  • DOI: https://doi.org/10.1007/BFb0120024

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52630-8

  • Online ISBN: 978-3-540-47085-4

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