Portfolio optimization aims to minimize risk and maximize return on investment by determining the best combination of securities and proportions. The variance in portfolio optimization models is typically used for a measure of risk. Over the last few decades, portfolio optimization utilizing a variety of risk measures has grown significantly, and many studies have been conducted. Therefore, this paper provides a systematic review of risk measures for portfolio optimization using bibliometric analysis and maps to analyze the evolution and trends of 682 articles published between 2000 and 2022. Throughout this analysis, communication networks among articles, authors, sources, countries, and keywords are explored. Furthermore, a classification of risks and risk measures were presented to demonstrate a comprehensive overview of the field, and the top 50 papers were analyzed to determine which risk measures were most often used in recent studies.

The aim of this study is to learn the effects of the value at risk (VaR) and the index of 30 largest companies (TEFIX 30) on the index of 30 large firms’ prices listed on Tehran Stock Exchange (TSE). This research study is based on analysis of libraries and analytical panel data and proposes a regression function where the index of 30 large companies’ prices is a linear function of VaR and TEFIX 30. The study collects the information of 90 publicly traded TSE firms over the period 2011-2013. The results have indicated that while the index of 30 large companies’ prices had a meaningful relationship with VaR but it had no meaningful relationship with TEFIX 30.

There are many researches on project selection field, but few of them have considered environmental criteria in their studies. Moreover, there are many articles in evaluating risk but there is no article that considers value at risk concept to evaluate the amount of risk in multi project selection. We propose a multi objective mathematical model to address a situation in which several projects are candidate to be invested completely or partially. Three objective functions are considered in this paper. The first objective maximizes sum of the net present value of pure cash flow obtained from selected projects. In this objective, we consider the factor of time and its impact on value of money. In addition, we use the concept of value at risk (VAR) as the present value for the first time in project selection problems. Although green projects are more interesting, there are few articles, which address environmental issues. Hence, we consider the objective, which are related to environmental issues as the final criterion. Multi-Objective Differential Evolution algorithm (MODE) algorithm is applied to solve a problem, which is known as robust and efficient algorithm. Then computational results are compared with solutions obtained by NSGA-II algorithm which is well-known algorithm in this field with respect to seven comparison metrics.

During the past few years, there have been several studies for portfolio management. One of the primary concerns on any stock market is to detect the risk associated with various assets. One of the recognized methods in order to measure, to forecast, and to manage the existing risk is associated with Value at Risk (VaR), which draws much attention by financial institutions in recent years. VaR is a method for recognizing and evaluating of risk, which uses the standard statistical techniques and the method has been used in other fields, increasingly. The present study has measured the value at risk of 26 companies from chemical industry in Tehran Stock Exchange over the period 2009-2011 using the simulation technique of Monte Carlo with 95% confidence level. The used variability in the present study has been the daily return resulted from the stock daily price change. Moreover, the weight of optimal investment has been determined using a hybrid model called Markowitz and Winker model in each determined stocks. The results showed that the maximum loss would not exceed from 1259432 Rials at 95% confidence level in future day.

This study determines the optimal investment portfolio in Tehran Stock Exchange (TSE) industries. For this purpose, a conditional capital asset pricing model (CAPM) with time-varying covariance, according to a Multivariate GARCH approach has been formulated. According to this conditional CAPM, the conditional variance-covariance matrix and mean of returns are calculated for some industries. By using the Mean-Value at Risk portfolio selection model, the optimum proportion is detected. Results showed that the Pharmaceutical Industry, Financial Group and Cement Industry have the most quotas in portfolio since they maintain the minimum variance and maximum return among all other industries.

Measuring risk of financial institutes and banks plays an important role on managing them. Recent financial turmoil in United States banking system has motivated banking industry to monitor risk factors more closely. In this paper, we present an empirical study to measure the risk of some private banks in Iran called Bank Mellat using Value at Risk (VaR) method. The proposed study collects the necessary information for the fiscal year of 2010 and analyses them using regression analysis. The study divides the financial data into two groups where the financial data of the first half of year is considered in the first group and the remaining information for the second half of year 2010 is considered in the second group. The implementation of VaR method indicates that financial risks increase during the time horizon. The study also uses linear regression method where independent variable is time, dependent variable is the financial risk, and the results confirm what we have found in the previous part of the survey.