Optimal investment under partial information

Tomas Bjork, Mark Davis () and Camilla Landén ()

Mathematical Methods of Operations Research, 2010, vol. 71, issue 2, 399 pages

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. Copyright Springer-Verlag 2010

Keywords: Portfolio; Optimal control; Filtering; Partial information; Stochastic control; Partial observations; Investment; 49N30; 60H30; 93C41; 91G10; 91G80 (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s00186-010-0301-x

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