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Explicit solution of a general consumption/investment problem

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Stochastic Differential Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 78))

Abstract

This talk shows how to solve a general consumption and investment decision problem in closed form. An investor seeks to maximize total expected discounted utility of consumption. There are N distinct risky investments, modelled by dependent geometric Brownian processes, and one riskless (deterministic) investment. The analysis allows for a general utility function and general rates of return. The model and analysis take into consideration the inherent nonnegativity of consumption and consider bankruptcy. The value function is determined explicitly, as are the optimal consumption and investment policies.

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Author information

Authors and Affiliations

  1. Columbia University, USA

    Ioannis Karatzas

  2. Carnegie-Mellon University, USA

    John P. Lehoczky

  3. University of Toronto, Canada

    Suresh P. Sethi

  4. Carnegie-Mellon University, USA

    Steven E. Shreve

Authors
  1. Ioannis Karatzas
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  2. John P. Lehoczky
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  3. Suresh P. Sethi
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  4. Steven E. Shreve
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Editor information

Norbert Christopeit Kurt Helmes Michael Kohlmann

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© 1986 Springer-Verlag

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Karatzas, I., Lehoczky, J.P., Sethi, S.P., Shreve, S.E. (1986). Explicit solution of a general consumption/investment problem. In: Christopeit, N., Helmes, K., Kohlmann, M. (eds) Stochastic Differential Systems. Lecture Notes in Control and Information Sciences, vol 78. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0041165

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  • DOI: https://doi.org/10.1007/BFb0041165

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16228-5

  • Online ISBN: 978-3-540-39767-0

  • eBook Packages: Springer Book Archive

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