multi-objective optimization

Pair trading strategy is one of the oldest and most common statistical arbitrage strategies. Pair formation is an important step in pair trading that examined manually and this method fails in the multivariate mode and does not consider conflicting goals in the problem structure. The main problem in this study is to present a method that creates multivariate pair combinations with multiple contradictory goals and focusing on the integration approach. Therefore, a combination of stocks optimized for two opposite objectives risk (mean-reversion) and return (spread variance) to form a set of profitable multivariate pair trading opportunities. The statistical population is companies listed on the Tehran Stock Exchange. The statistical sample limited by the need for high-frequency transactions from the top 50 companies. The problem developed in the form of a mixed integer-programming model (MIP), and due to non-convex constraints and exponential space, a multi-objective genetic algorithm used to obtain pair combinations. To achieve multiple goals, an advanced type of genetic algorithm; The Chaotic Non-dominated Sorting Genetic Algorithm (CNSGA-II) was used. The Chaos theory used to create the initial population of the genetic algorithm in order to obtain appropriate and high-precision solutions. Research has shown that the use of chaos theory can increase the degree of convergence in evolutionary algorithms. The results of the experiments of this study show that multi-objective pair trading strategies focusing on the integration approach have a significant advantage over the traditional single-objective model.

The novel theory of the portfolio optimization has developed based on the fundamental Markowitz model. The Markowitz model is unique in terms of theory, but its weaknesses prevent the use of this model in practice. In this model, the return rate is extracted based on past data, but in this research, future scenarios related to return rates has been used in the investment process. The Markowitz model and its subsequent generalizations are multi-objective. In this study, from the development approach of Zimmermann's multi-objective optimization approach, that has fuzzy like structure, has been used. Also, for confront with the uncertainties from a robust optimization approach based on minimization of regret, has been used. In other words, first describe Zimmermann's model by considering the scenarios and specific weighting combinations, for the two purposes of minimizing risk and maximizing return, and then the minimax regret solution has been calculated with respect to the considered scenarios and weighted combinations. In the end of this paper, in order to evaluate the performance and validation of the proposed model, it has been implemented in Tehran Stock Exchange.

To produce a proper reaction when confronted with market uncertainties (booms and busts), before making any investment decisions, investors and financial institutions tend to obtain some level of assurance about the market’s future and also the market’s probable feedback on their performance in the future. This study seeks to identify optimized robust portfolios with the best performance in the face of market uncertainties than can minimize the investors’ regret about their portfolio selection.

To create optimal portfolios, in the study, scenarios pertaining to various market situations based on daily returns of the Tehran Stock Exchange Price Index (TEDPIX) were designed, and the particle swarm optimization algorithm and minimax regret criterion were applied. This study also explored the application of multivariate objective functions and the Omega Conditional Value at Risk ratio as the fitting functions in particle mass optimization. To calculate optimal portfolios, the data from 50 companies on Tehran Stock Exchange (TSE) from 2009 to 2016 were analyzed. Also, the data from the year 2017 were evaluated as out of sample data.

Research findings indicated optimized robust portfolios in monthly periods had higher information ratios and lower tracking errors than the benchmark portfolios.

Making market scenarios and applying the minimax regret criterion improves the performance of optimized robust portfolios. Additionally, compared with the semi-variance benchmark model, applying the multi-objective function and Omega-Conditional Value at Risk ratio in portfolio optimization leads to improve performance of the robust portfolios.

In order to maintain the balance of cash flow between lenders and borrowers, banks have to use a financially appropriate ecosystem. When such a flow is rebated and or disrupted by non-performing loans (NPLs), life trends of banks and implementation of national economic policies are damaged seriously. Mis management and flexibility in lending and repaying off a loans are considered a drive force of NPLs.The aim of present research is to present a model for the optimization of bank loans portfolio under conditions of uncertainty, which is based on the robust scenario-based approach developed by Mulvey et al. uncertainty criteria set in this study include such economic factors as exchange rates, inflation, and systematic risks. This model has three objective functions: (1) increasing the returns of banks by increasing current loan, (2) decreasing the credit risk, and (3) mitigating the risk of bankruptcy based on Altman Financial Ratios, which are analyzed by using GAMS software. Using this model, bank managers based on the status and strength of each type of loan under normal circumstances and uncertainty can make the right decision to pay a certain amount of each type of loan according to the optimal limit, which reduces the credit risk and bankruptcy of the bank. The results also show that respectively systematic risk, inflation rate and exchange rate have the greatest impact on loan quality reduction.

In this paper, a multi objective multi stage stochastic model is proposed to portfolio selection. This model takes into account both the investment goal and risk control at each stage. A scenario generation method is proposed that acts as the basis of the portfolio management model. Scenarios for multistage portfolio management are proposed that use by consumption that rate of returns are not correlated during stages. One of the most important aspects of this model is using transaction cost in model and providing this ability that investors could add or withdrawal cash during time. In the end some numerical example are illustrated and model effectiveness proved. As is presented using stochastic programming with recourse and combination of this model with scenario generation model provides this possibility for investors to plan their medium and short term investing. As can be seen result of the model proved effectiveness of the model in financial markets. As result presented having such tool that investor could adjust his or her portfolio during time according to targets such as maximizing rate of return and minimizing risk of his or her decisions could bring powerful superiority in competitive financial markets.

In this study, the effective method of asset allocation characterized by risk control, cost reduction and out-performance with respect to the market benchmark has been investigated. In this regard, the optimal asset allocation in the core and satellite portfolio including the degree of risk aversion were studied. The core component of the portfolio represents an index fund selected by the use of a heuristic genetic based algorithm, which assures the level of risk-return realization comparable to the market index. The satellite component is consisted of selected mutual fund investment units and is managed actively in order to beat the market index.
An EGARCH model was used in order to simulate the required data, and a multi goal objective function as maximizing the excess return and minimizing the variance relative to the index was implemented for the modeling of the core-satellite problem.
The results of the analysis implies on the direct relationship between the degree of risk aversion and the weight allocated to the core component. The calculations also indicate the out-performance of the constructed portfolio relative to the market index and its good tracking ability based on criteria such as correlation and root mean squared error using out of sample data.