Optimal Investment under Partial Information
We consider the problem of maximizing terminal utility in a model where asset prices are driven by Wiener processes, but where the various rates of returns are allowed to be arbitrary semimartingales. The only information available to the investor is the one generated by the asset prices and, in particular, the return processes cannot be observed directly. This leads to an optimal control problem under partial information and for the cases of power, log, and exponential utility we manage to provide a surprisingly explicit representation of the optimal terminal wealth as well as of the optimal portfolio strategy. This is done without any assumptions about the dynamical structure of the return processes. We also show how various explicit results in the existing literature are derived as special cases of the general theory.
|Date of creation:||26 Feb 2010|
|Date of revision:|
|Note:||Published in: Mathematical Methods in Operations Research (2010),Volume 71, Number 2, pp 371-399|
|Contact details of provider:|| Postal: The Economic Research Institute, Stockholm School of Economics, P.O. Box 6501, 113 83 Stockholm, Sweden|
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- Feldman, David, 1992. "Logarithmic Preferences, Myopic Decisions, and Incomplete Information," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 27(04), pages 619-629, December.
- M. J. Brennan, 1998. "The Role of Learning in Dynamic Portfolio Decisions," Review of Finance, European Finance Association, vol. 1(3), pages 295-306.
- Jörn Sass & Ulrich Haussmann, 2004. "Optimizing the terminal wealth under partial information: The drift process as a continuous time Markov chain," Finance and Stochastics, Springer, vol. 8(4), pages 553-577, November.
- Brennan, Michael J & Xia, Yihong, 2001.
"Assessing Asset Pricing Anomalies,"
Review of Financial Studies,
Society for Financial Studies, vol. 14(4), pages 905-42.
- Brennan, Michael J. & Xia, Yihong, 1999. "Assessing Assets Pricing Anomalies," University of California at Los Angeles, Anderson Graduate School of Management qt3jx02532, Anderson Graduate School of Management, UCLA.
- Dothan, Michael U & Feldman, David, 1986. " Equilibrium Interest Rates and Multiperiod Bonds in a Partially Observable Economy," Journal of Finance, American Finance Association, vol. 41(2), pages 369-82, June.
- Gennotte, Gerard, 1986. " Optimal Portfolio Choice under Incomplete Information," Journal of Finance, American Finance Association, vol. 41(3), pages 733-46, July.
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