Scandinavian Working Papers in Economics

SSE/EFI Working Paper Series in Economics and Finance,
Stockholm School of Economics

No 739: Optimal Investment under Partial Information

Tomas Björk (), Mark H.A. Davis () and Camilla Landén ()
Additional contact information
Tomas Björk: Dept. of Economic Statistics, Stockholm School of Economics, Postal: Stockholm School of Economics,, P.O. Box 6501,, SE-113 83 Stockholm,, Sweden
Mark H.A. Davis: Imperial College, London, Postal: Department of Mathematics,, Imperial College,, London, SW7 2AZ,, England
Camilla Landén: KTH, Postal: Department of Mathematics, , Royal Insitute of Technology, , SE-100 44 Stockholm,, SWEDEN

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

JEL-codes: B26; C61

30 pages, February 26, 2010

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

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