geometrical approach of portfolio optimization

Risk aversion plays a significant and central role in investors’ decisions in the process of developing a portfolio.  In this portfolio optimization framework, we determine the portfolio that possesses the minimal risk by using a new geometrical method.  For this purpose, we elaborate an algorithm that enables us to compute any Euclidean distance to a standard simplex.  With this new approach, we can treat the case of portfolio optimization without short-selling in its entirety, and we also recover in geometrical terms the well-known results on portfolio optimization wi