Abstract: Abstract:Asset allocation problem in the condition of uncertainty is both important for academic research and individual investment.The traditional approach to asset allocation relies on Markowitz's paradigm which provides an elegant mathematical framework of an optimal asset allocation.Then Merton lays the foundation for dynamic asset allocation who considers an expected utility approach to study the optimal portfolio in a continuous time framework which is a breakthrough for modern finance theory.Cash, stock and bond in the generalized definition have been selected in this paper which are the most important three assets for investors and we obtain the optimal wealth and optimal portfolio weights of investors in the CRRA and HARA framework.The portfolio choice of a power utility that investors can maximize expected utility of wealth at a given investment horizon is considered.Closed form solutions are obtained in a dynamic portfolio optimization model.Also, the effects of inflation, risk preference, investment horizon on the asset allocation are analyzed.The results indicate that inflation which has an effect on the risk premium of stock and bond will finally influence the weights of them in the optimal portfolio.The weight of stock is not determined by the investment horizon, and the value is a constant when the inflation rate and risk preference are not changed.While the weight of bond and cash is determined by investment horizon, inflation rate and risk preference.In addition, the factors have great different influences on the asset allocation in the framework of CRRA and HARA.Especially, short sale will happen in the framework of HARA.

Key words: asset allocation, optimal portfolio, inflation, risk preference, investment horizon