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...Mathematics and statistics http www hrpub org doi ms markowitz random set its application to the paris stock market prices ahssaine bourakadi naima soukher baraka achraf chakir driss mentagui department of faculty sciences ibn tofail university kenitra morocco laboratory systems engineering high school technology fkih ben saleh sultan moulay slimane univesity beni mellal received march revised june accepted cite this paper in following citation styles a vol no pp b copyright by authors all rights reserved agree that article remains permanently open access under terms creative commons attribution license international abstract we will combine represents theory portfolio through estimation keywords lower bound based on mean variance analysis efficient frontier r software asset portfolios approach for statistical calculation which there are several optimization approaches subject classification msc p denote most known used modern namely s sharpe perold generally these methods minimization...