Optimal investment under partial information

  • Start Date: 10/04/2007
  • End Date: 10/05/2007

Thomas Bjork (Stockholm School of Economics)


University of British Columbia


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 semi-martingales. The only
information available to the investor is the 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 on the 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.

Other Information: 

MITACS Math Finance Seminar 2007