‎‎The Portfolio optimization problem, including Portfolio selection, typically aims to maximize return and minimize risk. In this paper, we discuss about increasing use of stochastic Portfolios in investments and aim to create optimal Portfolios. It follows the relative wealth process of these Portfolios, outperforms the market Portfolio over sufficiently long time-horizons. In this regard, initially, a model of the market is presented by the stochastic Portfolio theory (SPT) and features like Growth rate, Excess growth rate are mentioned. Then, functionally-generated Portfolios are defined by using diversity weighted Portfolios with parameters p ∈ (0, 1), p < 0 and combination of them. Finally, by obtaining the daily closing price of 10 stocks in Tehran Stock Exchange (TSE) ,the performance of diversity weighted Portfolios is investigated.

The Markowitz’s optimization problem is considered as a standard quadratic programming problem that has exact mathematical solutions. Considering real world limits and conditions، the Portfolio optimization problem is a mixed quadratic and integer programming problem for which efficient algorithms do not exist. Therefore، the use of meta-heuristic methods such as neural networks and evolutionary algorithms has been an important issue in the literature of Portfolio optimization. This study considers the problem of finding the efficient frontier associated with the standard mean-variance Portfolio optimization model and presents a heuristic algorithm based upon particle swarm optimization for finding the cardinality constrained efficient frontier. The test data set is the daily prices of 20 companies from March 2006 to September 2008 from the TEPIX in Iran. The results show that PSO is successful in constrained Portfolio optimization to find the optimum solutions in all levels of risk and return.

Finding the best way to optimize the Portfolio after Markowitz's 1952 article has always been and will continue to be one of the concerns of activists in the investment management industry. Researchers have come up with different solutions to overcome this problem. The introduction of mathematical models and meta-heuristic models is one of the activities that has influenced Portfolio optimization in recent decades. Along with the growing use of Portfolios and despite its rich literature, there are still many unanswered issues and questions in this area. Also, Iranian capital markets, as emerging markets, require native research to answer these questions and issues. The purpose of this study is to provide a useful and effective tool to assist professionals and researchers in Portfolio selection theory. This study, while comprehensively reviewing the literature on the subject and the developments and expansions made in the area of Portfolio selection and optimization, reviews the types of problems and optimization methods.

In this paper, we discuss some of the concepts of robustness for uncertain multi-objective optimization problems. An important factor involved with multi objective optimization problems is uncertainty. The uncertainty may arise fromthe estimation of parameters in the model, error of computation, the structure of a problem, and so on. Indeed, some parameters are often unknown at the beginning of solving a multi-objective optimization problem. One of the mostimportant and popular approaches for dealing with uncertainty is robust optimization. Markowitz's Portfolio optimization problem is strongly sensitive to the perturbations of input parameters. We consider Markowitz's Portfolio optimization problem with ellipsoid uncertainty set and apply set-based minmax and lower robust efficiency to this problem. The concepts of robust efficiency are used in the real stock market and compared to each other. Finally, the increase and decrease effects of uncertainty set parameters on these robust efficient solutions are verified.