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The Economic Research Institute, Stockholm School of Economics SSE/EFI Working Paper Series in Economics and Finance

No 739:
Optimal Investment under Partial Information

Tomas Björk (), Mark H.A. Davis () and Camilla Landén ()

Abstract: 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.

Keywords: Optimal control; investment theory; filtering; (follow links to similar papers)

JEL-Codes: B26; C61; (follow links to similar papers)

30 pages, February 26, 2010

Published in: Mathematical Methods in Operations Research (2010),Volume 71, Number 2, pp 371-399

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