  We calculate explicitly the optimal strategy for an investor with exponential
utility function when the stock price follows an autoregressive Gaussian
process. We also calculate its performance and analyse it when the trading
horizon tends to infinity. Dependence of asymptotic performance on the
autoregression parameter is determined. This provides, to the best of our
knowledge, the first instance of a theorem linking directly the memory of the
asset price process to the attainable satisfaction level of investors trading
in the given asset.
