CERTAINTY EQUIVALENCE AND LOGARITHMIC UTILITIES IN CONSUMPTION/INVESTMENT PROBLEMS

We investigate an optimal consumption/investment decision problem with partially observable drift. Logarithmic utilities are shown to be necessary and sufficient for the certainty equivalence principle to hold. For the sufficiency part of the proof, we allow a general stochastic structure about the unobservable drift. On the other hand, a simple Bayesian structure is assumed for the necessity part in order to utilize the Hamilton-Jacobi-Bellman equations.