Kazem Nouri - Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences
Parisa Sabet - Semnan University, Semnan, Iran

Optimal alloction of capital to investment and minimizing the risk of investmen , most investors one of the main objective . The problem of allocating funds into a given set of investable assets is known as portfolio selection. In this paper, we derive a portfolio optimization model by minimizing upper and lower bounds of loss probability. Based on the bounds, two fractional programs are derived for constructing portfolios, where the numerator of the ratio in the objective includes the value-at-risk (VaR) or conditional value-at-risk (CVaR) while the denominator is any norm of portfolio vector. Some computational experiments are conducted on real stock market data, demonstrating that the CVaR-based fractional programming model outperforms the empirical probability minimization

Portfolio optimization, Loss probability, CVaR, Fractional programming