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We calculate explicitly the optimal strategy for an investor with exponentialutility function when the stock price follows an autoregressive Gaussianprocess. We also calculate its performance and analyse it when the tradinghorizon tends to infinity. Dependence of asymptotic performance on theautoregression parameter is determined. This provides, to the best of ourknowledge, the first instance of a theorem linking directly the memory of theasset price process to the attainable satisfaction level of investors tradingin the given asset.

An explicit solution for optimal investment problems with autoregressive prices and exponential utility