In this dissertation a four moment asset allocation model is proposed. Some assumptions are made in order to simplify the optimization model and to obtain a closed form solution for the optimal portfolio. In particular, the key assumption concerns the representation of skewness and kurtosis. The obtained optimal portfolio is a generalization of the classical two moments optimal portfolio, see Markowitz (1952). This generalization permits to write the optimal portfolio as the sum of three portfolios: the first one is the meanvariance optimal portfolio, the second one depends on the skewness only and the third one on the kurtosis only. Moreover, the efficient frontier and a four funds separation theorem has been derived in the four moments framework.