Portfolio selection is one of the most important financial and investment issues. Portfolio selection seeks to allocate a predetermined capital (wealth) over one or multiple time periods between assets and stocks in a such way that the wealth of investor (portfolio owner) is maximized the risks are minimized. In the paper, we first propose a mathematical programming model for Portfolio selection to maximize the minimum amount Sharpe ratios of portfolio in all periods (max-min problem). Then, due to the uncertain property of the input parameters of such a problem, a Robust possibilistic programming model (based on necessity theory) has been developed, which is capable of adjusting the Robust degree of output decisions to the uncertainty of the parameters. The proposed model has been tested on 27 companies active in the Tehran stock market. At the end, the results of the model demonestrate the good performance of the Robust possibilistic programming model.

one of the most important financial and investment issues is Portfolio selection, that seeks to allocate a predetermined capital (wealth) over one or multiple periods between assets and stocks in such a way that the wealth of investor (portfolio owner) is maximized and, Simultaneously, its risk minimized. In the paper, we first propose a mathematical programming model for Portfolio selection to maximize the minimum amount of Sharpe ratios of the portfolio in all periods (max-min problem). Then, due to the uncertain property of the input parameters of such a problem, a Robust possibilistic programming model (based on necessity theory) has been developed, which is capable of adjusting the Robust degree of output decisions to the uncertainty of the parameters. The proposed model was tested on 27 companies active in the Tehran stock market. In the end, the results of the model demonstrated the good performance of the Robust possibilistic programming model.

Many portfolio Optimization problems deal with allocation of assets which carry a relatively high market price. Therefore, it is necessary to determine the integer value of assets when we deal with portfolio Optimization. In addition, one of the main concerns with most portfolio Optimization is associated with the type of constraints considered in different models. In many cases, the resulted problem formulations do not yield in practical solutions. Therefore, it is necessary to apply some managerial decisions in order to make the results more practical. This paper presents a portfolio Optimization based on an improved knapsack problem with the cardinality, floor and ceiling, budget, class, class limit and pre-assignment constraints for asset allocation. To handle the uncertainty associated with different parameters of the proposed model, we use Robust Optimization techniques. The model is also applied using some realistic data from US stock market. Genetic algorithm is also provided to solve the problem for some instances.