Abstract: The standard portfolio selection theory assumes that investors exactly know the security parameters,neglecting the effect of estimation risk induced by parameter uncertainty on asset portfolios.This paper investigates a continuoustime portfolio selection problem with parameter uncertainty and learning for aninvestor with CRRA utility.By using the martingale method,we derive a closeform expression for the optimal portfolio strategy.Based on the result,by combining a comparative static analysis with the data of China Security Market,we study the effect of the investment horizon and the initial belief of the investor on the optimalstrategy.

Key words: dynamic portfolio selection, utility maximization, parameteruncertainty, Bayesian learning