  The question addressed in this paper is the performance of the optimal
strategy, and the impact of partial information. The setting we consider is
that of a stochastic asset price model where the trend follows an unobservable
Ornstein-Uhlenbeck process. We focus on the optimal strategy with a logarithmic
utility function under full or partial information. For both cases, we provide
the asymptotic expectation and variance of the logarithmic return as functions
of the signal-to-noise ratio and of the trend mean reversion speed. Finally, we
compare the asymptotic Sharpe ratios of these strategies in order to quantify
the loss of performance due to partial information.
