In this paper, we solve the multi-period portfolio optimization problem under new assumptions. Recently, the authors examined some distributions instead of Gaussian to fit returns to improve the optimization problem and indicated, by Kolmogorov-Smirnov test, that the Kernel density estimator is the best one. In the present paper, we consider the most appropriate distribution of each asset in each period to fit return. Moreover, in order to optimize the solutions, we use piecewise linear interpolation of the empirical distribution. Furthermore, we show that how one may plan for future investments using historical data and AR(1)-GARCH(1,1) model under new assumptions.

Keywords: Multi-period Portfolio Optimization‎, ‎Probabilistic Risk Measure‎, ‎Kernel Distribution Estimator‎, Piecewise ‎Linear Interpolation‎, AR(1)-GARCH(1, 1) Model.

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