  This paper presents an optimal allocation problem in a financial market with
one risk-free and one risky asset, when the market is driven by a stochastic
market price of risk. We solve the problem in continuous time, for an investor
with a Constant Relative Risk Aversion (CRRA) utility, under two scenarios:
when the market price of risk is observable (the {\em full information case}),
and when it is not (the {\em partial information case}). The corresponding
market models are complete in the partial information case and incomplete in
the other case, hence the two scenarios exhibit rather different features. We
study how the access to more accurate information on the market price of risk
affects the optimal strategies and we determine the maximal price that the
investor would be willing to pay to get such information. In particular, we
examine two cases of additional information, when an exact observation of the
market price of risk is available either at time $0$ only (the {\em initial
information case}), or during the whole investment period (the {\em dynamic
information case}).
