The mean-variance formulation by Markowitz for modern optimal portfolio selection has been analyzed for a single period. This analysis is extended to obtain an analytical optimal solution to the mean-variance formulation in multi-period portfolio selection. An efficient algorithm is proposed for finding an optimal portfolio policy to maximize a utility function of the expected value and the variance of the terminal wealth. Further, a concept named safety-first is exploited for dynamic multi-period portfolio selection problems. In this case, an optimal multi-period portfolio policy is sought to minimize the probability that the terminal wealth is below a preselected level. Specifically, an analytical solution is achieved for this multi-period safety-first formulation, which makes the derived investment strategy an easy implementation task.;Index terms. Dynamic portfolio selection, dynamic programming, mean-variance formulation, stochastic control, utility function, pricing model and theory, certainty versus uncertainty on financial markets.
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