Skip to main content
SpringerLink
Log in

An introduction to optimal consumption with partial observation

  • Conference paper
Mathematical Finance

Part of the book series: Trends in Mathematics ((TM))

Abstract

We give a short introduction to some of the theory and methods involved in stochastic control with partial observation. As an illustration we use the stochastic maximum principle and the Kalman-Bucy filter to solve explicitly a problem about optimal consumption in an economy where the mean relative growth rate is only observed indirectly (partially).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. Bensoussan: Perturbation Methods in Optimal Control. J. Wiley & Sons 1988.

    Google Scholar 

  2. A. Bensoussan: Stochastic Control of Partially Observable Systems. Cambridge Univ. Press 1992.

    Book  Google Scholar 

  3. M.H.A. Davis: Linear Estimation and Stochastic Control. Chapman and Hall 1977.

    Google Scholar 

  4. R.J. Elliott, H. Geman and B.M. Korkie: Portfolio optimization and contingent claim pricing with differential information. Stochastics and Stochastics Reports 60 (1997), 185–203.

    MathSciNet  MATH  Google Scholar 

  5. G. Kallianpur: Stochastic Filtering Theory. Springer-Verlag 1980.

    Google Scholar 

  6. Y. Kuwana: Certainty equivalence and logarithmic utilities in consumption/investment problems. Math. Finance 5 (1995), 297–309

    Article  MathSciNet  MATH  Google Scholar 

  7. B. Øksendal: Stochastic Differential Equations. Fifth edition. Springer-Verlag 2000.

    Google Scholar 

  8. S. Peng: A general stochastic maximum principle for optimal control problems. SIAM J. Control & Opt. (1990), 966–979.

    Google Scholar 

  9. J. Yong and X.Y. Zhou: Stochastic Controls. Springer-Verlag 1999.

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. INRIA, Domaine de Voluceau-Rocquencourt, B.P. 105, Le Chesnay Cedex, F-78153, France

    David Lefèvre & Bernt Øksendal

  2. Dept. of Mathematics, University of Oslo, P. O. Box 1053 Blindern, Oslo, N-0316, Norway

    Bernt Øksendal

  3. Norwegian School of Economics and Business Administration, Helleveien 30, Bergen, N5045, Norway

    Agnès Sulem

Authors
  1. David Lefèvre
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bernt Øksendal
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Agnès Sulem
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Fakultät für Mathematik und Informatik, Universität Konstanz, Postfach 5560, Konstanz, D-78434, Germany

    Michael Kohlmann

  2. Department of Mathematics, Fudan University, Shanghai, 200433, China

    Shanjian Tang

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer Basel AG

About this paper

Cite this paper

Lefèvre, D., Øksendal, B., Sulem, A. (2001). An introduction to optimal consumption with partial observation. In: Kohlmann, M., Tang, S. (eds) Mathematical Finance. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8291-0_22

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-8291-0_22

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9506-4

  • Online ISBN: 978-3-0348-8291-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation