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This paper investigates an optimal mean-variance portfolio selection model. The model is formulated with a free risky asset, a risky asset and a liability under discontinuous prices which follow jump-diffusion processes. Moreover, the short-selling of stock is prohibited. The correlation between the risky asset and the liability is considered. The corresponding Hamilton-Jacobi-Bellman equation of the problem is presented. The solution of the HJB equation based on the theory of stochastic LQ control. The optimal dynamic strategy and the efficient frontier in closed forms are derived explicitly.

Portfolio is a financial concept to combine several stocks to reduce the risks and improve the profits. To choose the basic members of portfolio, we can group similar stocks into one cluster and then choose representative stock from each cluster. In this paper, we focus on the method of choosing representative stocks in clusters. The ordinary representative of a cluster is often the center of that cluster. We propose a new cluster representative method MDR (maximum distance representatives). In our method MDR, we choose the stocks which has maximum distance with other representatives. MDR can construct a more diverse portfolio than center method. The effectiveness of cluster representative selection methods can be evaluated by an index IBEF based on the concept of efficient frontier. Our experiments show that MDR can effectively improve the efficient frontier, which means MDR can bring more profits than center representative method at the same risk level.

The aim for balance between risk and reward in investment portfolios often requires studying the diversification contribution of its constituents. This objective requires to specify whether investors can extend their exposure in certain asset classes and benefit their portfolios in a statistically significant way. In this paper, we address this issue of diversification in the context of cryptoasset portfolios and examine whether their risk-adjusted performance can be enhanced through seeking exposure into the commodities class. For an equally-weighted portfolio of five cryptoassets, we first consider the addition of physical gold, as conceptualised by the CoinShares Gold and Cryptoassets Index, a diversified, monthly-rebalanced index that seeks exposure to both asset classes. We further consider modifying the index composition by replacing physical gold with a basket of five commodities. Mean-variance spanning tests reveal that the addition of physical gold in the original cryptoasset portfolio translates to a significant shift in the efficient frontier, both in terms of the global minimum variance and the tangency portfolios. Additionally, expanding the exposure in the commodity side confirms a statistically significant improvement, with the diversification benefit arising from a shift in the tangency portfolio. We further generate a number of price paths for the original index, the modified index and their components, according to a Dynamic Conditional Correlation GARCH specification, to assess the efficiency of the index weighted risk contribution scheme. Results demonstrate a superior performance of the two indices when compared against their constituents in terms of Omega ratio. The modified index appears more appropriate for investors that seek higher annual returns, while the original composition would be more appropriate for individuals with moderate annual return goals.

The Markowitz model is an established approach to portfolio optimization that constructs efficient frontiers allowing users to make optimal tradeoffs between risk and return. However, a limitation of this approach is that it assumes future asset returns and covariances will be identical to the asset's historical data, or that these model parameters can be accurately estimated, a notion which often does not hold in practice. Markowitz efficient frontiers are square root second-order polynomials that can be represented by three parameters, thus providing a significant dimensionality reduction of the lookback covariances and growth of the assets. Using this dimensionality reduction, we propose an extension to the Markowitz model that accounts for the nonstationary behavior of the portfolio assets' return and covariance without the necessity to forecast the complex covariance matrix and assets growths, something that has proven to be extremely difficult. Our methodology allows users to forecast the three efficient frontier coefficients using a time-series regression. By observing similar efficient frontiers, this forecasted efficient frontier can be used to select optimal assets mean-variance tradeoffs (asset weights). For exploratory testing we employ a set of assets that span a large portion of the market to demonstrate and validate this new approach.

Selecting the number of assents to obtain the maximized expected return under the possible lowest risk is the main concern of portfolio optimization problems. Optimization algorithms -multi/many-objective- are evaluated to find the desired/possible level of investment. Converging to the best possible asset set and -if possible- distribution of the many possible solution sets for an efficient frontier is expected as the result of the multi/many-objective optimization algorithms. Obtaining an accurate and well-distributed set of solutions is the main motivation. Hence, in this paper, two initialization approaches are proposed for multi/many-objective optimization algorithms to obtain a better convergence and distribution solution set for the portfolio optimization problem. The initial population set is composed of the assets with the largest income and binary combinations of the assets where their sum returns the maximum income. These proposed approaches are integrated with eight different optimization algorithms and the performance of the algorithms is compared with respect to the convergence and diversity metrics.

This paper introduces Portfolio Theory, a tool in finance, as a solution to power allocation transmitters in coordinated multi-point (CoMP) systems to combat the link loss and variation of directional millimeter-wave (MMW) signals. With this theory, the mean-variance performance of the receiving power in CoMP transmission can be optimized by choosing portfolios along the efficient frontier. The method is experimentally demonstrated in a 2x1 CoMP transmission system operating at 28 GHz, in which the average receiving power is improved by 20% and the power deviation is improved by 16% by using the proposed method.

This paper considers portfolio optimization whose goal consists in finding a set of efficient portfolios regarding the framework of the Mean-Variance Analysis. Our work utilizes the GPU’s computing capabilities to accelerate the computation within portfolio optimization. In particular, we present a nontrivial GPU-accelerated method to produce a set of minimum variance portfolios for a given target range of expected returns under the basic constraints of the framework. We evaluate the experimental performance of the method by synthesizing an implementation using CUDA. The experimental results show that our implementation performs substantially faster than its implementation counterpart using CLAPACK with respect to the task of simulating the efficient frontier on large data sets with the number of assets in the range of hundreds.

Robust regression has been a common method used to solve some portfolio selection problem by using traditional ordinary least square estimation (OLS). However, the outliers in the realistic data often break the data consistency rules which make the ordinary least square estimation lose efficacy. Here, the Exponential Squared Loss (ESL) robust regression is considered to eliminate the influence of outliers. By adjusting the square loss function into ESL function and adaptive LASSO penalty function, the parameters estimation accuracy is improved thereby, reducing the impact of outliers in historical returns on the investment portfolio decision. This article attempts to verify the robustness of the single index model by using Shenzhen A-share market data. The result indicates the advantage of the ESL robust regression by comparing the estimation accuracy of the ESL robust estimation with OLS estimation and M-estimation. Finally, the portfolio efficient frontier reveals the stability of ESL robust regression in the single index modeInt.

Clustering is an unsupervised learning method to discover meaningful information by grouping similar objects together. It is a great challenge to valuate the results of stock clustering. In this paper, we propose a specific index IBEF(Index Based on Efficient Frontier) to evaluate the results of stock clustering based on the concept of efficient frontier. IBEF is defined by the difference between two efficient frontier curves. One curve is built by all stocks and the other curve is built by center stock of each cluster. If the clustering result is good, the two curves are close to each other and IBEF value will be small. Our experiments on different correlation coefficients and clustering methods show that IBEF is a proper validity index comparing with other indexes.

This article addresses the challenge of project portfolio selection. Due to the scarcity of resources in companies, decision makers need to select a subset of projects to be executed, from a list of projects to be developed. The return and risk assessment methods, widely disseminated in the literature, lead to a list of efficient portfolios, but it does not indicate exactly which one should be executed. With the application of three different multi-criteria selection methods (MCDM) - TOPSIS, VIKOR and PROMEHTEE II, combined with a return risk evaluation method (Mean-Gini), this work proposes a way to indicate the best portfolio of projects to be executed.

Describing future security returns as fuzzy random variables, we present a multi-objective multi-period port-folio model by considering multiple decision criteria and real-world constraints. An intelligent hybrid algorithm is then proposed to solve the presented model. In this algorithm, we devise a novel way of searching the Pareto-optimal solutions, train a Simulated Annealing Resilient Back Propagation (SARPROP) neural network for objectives approximation, and use fuzzy random simulation to generate the training dataset. The proposed algorithm is compared with the one generated by integrating NSGA-II, SARPROP neural network and fuzzy random simulation. The results demonstrate that our algorithm significantly outperforms the compared one in terms of the running time and the quality of obtained efficient frontier. To improve computational efficiency, we adopt MPI to parallelize our algorithm. The parallel algorithm is tested on different processors and its scalability is verified.

Portfolio optimization aims to pick risky assets to meet the goal of maximizing the return and minimizing the risk. One should model the best combination of assets by striving the optimal relationship between risk and return for an appropriate investor even when the constraints are present. This paper aims to study the risk measure Conditional Value At Risk with constraints, that are added in a portfolio and are analyzed in the optimization problem. It also focuses on how will the portfolio work when a threshold value $L(\alpha)$:- CVaR is fixed. The dataset was taken from YAHOO Finance consisting of weekly historical prices were implemented.

Machine learning algorithms such as Support Vector Machine (SVM) and Artificial Neural Network (ANN) are used for machine trading. The problem with SVM and ANN is that it is difficult to determine appropriated features for both models; moreover, it is also time consuming to perform backpropagation for ANN when a number of both features and data increase. However, machine trading is not confined only these two algorithms, but also time series models. In this study, we will employ time series models namely Autoregressive Integrated Moving Average (ARIMA) and Holt – Winters’ Exponential Smoothing (HW) as the guidance for trading since time series models only require time series as an input. We will perform time series analysis to snatch the trading opportunity in the Stock Exchange of Thailand (SET). There are fifty companies on the list of SET50 index; we will choose five amongst them to invest measured by Sharpe Ratio; the top five from this measurement will be selected as invested assets in simulated portfolio. Furthermore, the well-known portfolio optimization framework by Harry Markowitz will be used to ensure that the combination of the invested assets is located on the efficient frontier; the result from this study is favorable as the return generated by these activities outperforms market return; furthermore, manipulating time series into different time lags yields higher return and as well as combining both ARIMA and HW models to help predict stock prices also improves power of prediction of time series models. This study will help retail investor who has limited resource overthrow bias and intuition throughout investment decision process ranging from finding the stocks for investment to capturing market movement for trading opportunity.

When investing in the stock market, the first problem and one of paramount importance which investors have to face is making the proper stock selection. Selecting the stocks that simultaneously offer high return and low risk is a difficult problem that is worth investigating. However, the traditional risk calculation based on the modern portfolio theory (MPT) of portfolios has some defects. The MPT method requires the calculations of every relationship between each pair of stocks in the portfolio, entailing high computation complexity, which grows exponentially with the increased number of stocks. Besides, the traditional calculation is unable to calculate the coefficient of variation, and merely considers the relationship between each pair of stocks, so it cannot accurately assess portfolio risk. Therefore, this paper proposes a novel method, funds standardization, and utilizes it to represent the portfolio return and calculate portfolio risk. The fluctuation of portfolio funds standardization shows not only the relationships between each pair of stocks, but also the interactions among all stocks. Hence, utilizing funds standardization can accurately assess portfolio risk and completely represent the mood swings of investors. Compared with the traditional method, the proposed method significantly reduces the computation complexity because the complexity does not increase when the portfolios stock number increases. We combine the genetic algorithm, Sharpe ratio and funds standardization to find the optimal portfolio. In addition, we utilize the sliding window to avoid the over-fitting problem, which is common in this field, and test the effect of all kinds of training and testing periods. The experimental results show that the portfolio can spread the risk effectively, and that the portfolio risk can be assessed accurately by utilizing the funds standardization. Comparing with the traditional method, our method can identify the optimal portfolio efficiently and establish a portfolio that has lower risk and stable return.

Portfolio optimization using bank deposit and loan is formulated as a chance constrained problem in which a non-risk asset called bank deposit is included in the portfolio and the borrowing money called bank loan can be invested in risk assets. The chance constrained problem is transformed into an equivalence problem. Then an Adaptive Differential Evolution using Directed mutation (ADED) is proposed and applied to the equivalence problem. Furthermore, in order to cope with large scale instances, ADED is extended to group-based ADED called ADED4G. ADED4G divides the feasible region of the chance constrained problem into four areas and executes ADED in each of the areas simultaneously. Experimental results show that both ADED and ADED4G are excellent. Besides, the practical use of bank deposit and bank loan improves the efficient frontier.

An automated process for selecting sites for new wind farm installations is proposed. The region of interest is divided into a 1-km-square mesh, and geographical data such as altitude and wind speed are used to sort the mesh cells into regions that are feasible for wind farm installations. Before grouping the meshes, feasible meshes for constructing wind farms are extracted using a set of constraints. We tested two different constraints for grouping the feasible areas, either by maximizing the annual mean wind speed or by minimizing the covariance between the power outputs of each cell in the group. The first strategy is more attractive if the goal is to meet an expected level of power output each year, while the second strategy is intended to supply the most-stable power. Portfolio theory was then applied to the evaluate efficient-frontier curves of the two site-selection results from the mean and variance of the total expected power outputs. The analysis showed that grouping unit areas to maximize average wind speed most effectively suppresses variance in the expected output of an installation, and efficiently distributes the optimum wind farm locations.

In order to build a portfolio selection model for a robo-advisor, which can be used on ETFs of mainland China and get the efficient frontier, a number of models based on the mean-variance model are studied and analyzed experimentally, the results show that the hybrid model using Hopfield neural network and genetic algorithm can output efficient frontier better than others. Based on this, exponentially weighted moving average/covariance are applied to adjust the model’s inputs, that is, the mean and covariance of assets’s return rate. Experiments were conducted using the collected transaction data of ETFs, the results show that after the adjustment the model can know future performance of portfolios better based on long-term historical transaction data.

The problem of portfolio optimization is a research topic that is quite widely discussed in the financial sector. The first model in this problem is the mean-variance model that focuses on expected return and risk without considering the constraints contained in the real problem. In this paper, a portfolio optimization model with real constraints which is commonly known as the Mean-Variance Cardinality Constrained Portfolio Optimization (MVCCPO) model is considered. The e-New Local Search based Multi-objective Optimization Algorithm (e-NSLS) and Multi-objective Covariance based Artificial Bee Colony (M -CABC) algorithm are used to solve portfolio optimization problem on datasets involving up to 225 assets. Obtained results are compared with the unconstrained efficient frontier of the corresponding data sets. The numerical simulations state that e-NSLS algorithm gives a better solution than M-CABC, where the solutions produced by e-NSLS are nearer to the corresponding unconstrained efficient frontier than the solutions generated by M-CABC.

In recent years, with the vigorous development of the new energy industry in the world, distributed photovoltaics (PV) have strongly penetrated the international energy markets at exponential growth rates, and a large number of electric vehicles (EVs) have been used mainly driven by policies. The use of EVs and distributed PV would lead to an increase in load uncertainty. Hence, a new day-ahead portfolio optimization model for a power supply company with distributed PV considering EVs was developed. The model contains risks depending on market price fluctuation and load uncertainty caused by EVs load, conventional load and distributed PV's output, considering the expected cost of errors, and helping to determine an optimal quantity of power to be obtained from distributed PV's output and different electricity markets. This paper analyses the efficient frontier of conditional value-at-risk (CVaR) and the influence of different EVs market penetration levels and distributed PV's output on the portfolio strategy.

Indonesia is an Archipelagic State (maritime continent) with a strategic position and high potential in natural resources. Satellite technology is expected to provide answers in managing spatial-based natural resources. This paper presents a Simple Multi Attribute Rating Technique (SMART) method for organizing and evaluating activities of a big and complex problem solution. To illustrate this method, a case study that deal with vendor selection of satellite systems will be discussed in this paper. The activity is integrated in a decision support system (DSS) which is using of the SMART method to determine vendor rankings and an efficient frontier. SMART method is used in this group decision making process because it can divide complex problems into sets of uncomplicated analysis and therefore able to directly influence the understanding of stakeholders on the process used in finding solutions. This group decision making process involves many stakeholders. Satellite system vendor selection is an important issue as the satellite system is a long-term investment commitment for the government. And also the success of satellite application services can be influenced by the vendor selection result. Moreover, the vendor selection of a satellite system is involving multiple stakeholder with multiple criteria decision-making issue. A systematic approach to assess priorities based on the inputs of several stakeholders can improve the group decision-making process. The paper will illustrate that several decision-makers with different conflicting objectives can use the SMART method to arrive at a consensus. This case study indicates that SMART method can be used to improve group decision making in vendor selection that meets stakeholder criteria. This paper found that the proposed SMART model can reduce the time required for vendor selection and the decision-making process become more systematic. A procedure for selecting the number of providers shall be made in a process which presents as an efficient frontier analysis. Finally, results of criteria and cost benefit analysis design scenarios of satellite industry using SMART method are discussed and we will make some conclusions.

Portfolio selection problem that deals with the optimal allocation of capital is a well-known hard optimization problem in the domains of economics and finance. Basic version of the problem is multi-objective since it deals with maximization of return with simultaneous minimization of risk. Additional real world constraints, including cardinality, make the problem even harder. Many techniques and heuristics have been applied to this intractable optimization problem, however swarm intelligence algorithms have been implemented only few times for this task, even though they are known to be very successful for that class of problems. In this paper, we hybridized artificial bee colony algorithm with elements inspired by genetic algorithms to obtain better balance between intensification and diversification, especially during late stages, and applied the proposed improved algorithm to the cardinality constrained mean-variance version of the portfolio selection problem. Experimental results on standard benchmark datasets from five stock indexes and comparative analysis with other cutting edge algorithms have shown that our proposed algorithm achieved better results considering all relevant metrics i.e. mean Euclidean distance between standard efficiency frontier and heuristic efficiency frontier from sets of Pareto optimal portfolios obtained by tested algorithms, mean return error and variance of return error.

This paper evaluates relative performances of power distribution utilities of 28 states of India for the year 2012–13, through application of Data Envelopment Analysis (DEA). Benchmark utilities have been identified for each non-frontier utilities to emulate the best practices for improvement. Further slack analysis is carried out to identify the root causes of inefficiencies of the utilities lying away from the frontier. About 86% of the distribution utilities are found to be digressing from efficiency frontier. The main cause of the inefficiencies is observed to be excessive distribution line length compared to the revenue realized and number of consumers served by those. Specific recommendations have been made for the policy level changes required for improving the overall performance of the distribution utilities and socio-economic standing of the rural population of India.

This paper deals with a multi-period portfolio selection problem with fuzzy returns. A mean-variance-skewness model for multi-period portfolio selection is presented by taking into account four criteria viz., short and long term returns, dividends, liquidity and number of assets in the portfolio. The return and risk level are measured by interval numbers in the proposed model. Furthermore, an intelligent algorithm is designed to obtain the optimal portfolio strategy. Finally, a numerical example is provided to illustrate the efficiency of the proposed model and the designed algorithm.

The paper is to establish a feasible evaluating indicator system for university endowment funds based on principle component analysis. According to information provided by the reference index system from nearly 8000 schools were selected, the 16 indicators were proposed and 1340 schools were selected as the alternative school for investment objectives. By using data envelopment analysis (DEA), 30 schools were selected to invest from 1340 schools, and the optimal investment strategies of those 30 schools in the next five years were given. For the non DEA effective decision-making units in data envelopment analysis, T projection transformation in the efficiency frontier were used, which made the point input and output combined to be data envelopment analysis efficiency. The model was applied to the investment for University Endowment Funds, which verified effectiveness and advantage.

This paper is a comparative study of metaheuristics in the portfolio optimization problem. The objective is to present the results obtained with the meta-heuristics Cat Swarm Optimization CSO, bat algorithm BA and particle swarm optimization PSO applied to the cardinality constrained efficient frontier model CCEF, the results obtained has compared with those done using the unconstrained efficient frontier model UEF.

In the literature, researchers usually assume that late outpatients are not accepted by hospitals. Although this assumption simplifies models by making them analytically tractable, it rarely holds true for most clinics. This paper introduces a back row policy for late outpatients, and evaluates performance improvements from its incorporation into commonly studied appointment rules. We use simulations to obtain the expectations of patients' waiting time and doctor's idle time, and present the results in the form of efficient frontier. Through pre-established procedures, we are able to identify the optimal rule of appointment scheduling under given parameters.

The mean-variance portfolio model assumes that the returns follow a multivariate normal distribution. Unfortunately in actual financial markets, the empirical distribution of asset returns may in fact be asymmetric or multivariate elliptically symmetric with heavier tails. Therefore, the resulting optimal portfolio by this model will be heavily biased. For this reason, in this paper, we construct a robust mean-variance portfolio that has better stability performances. The robust portfolio is constructed using certain robust estimator, i.e. Constrained M-Estimator. Based on simulation and empirical results, we can conclude that our proposed robust portfolios are better than classical portfolios in all cases investigated.

It is impossible for any investor to estimate future returns correctly by historical data of assets. So a forecasting methods by experts' judgement based on historical are given to estimate the future returns of assets. Taking into account that investor sentiment has an important influence on stock price, a model for portfolio selection with investors sentiment is proposed under fuzzy and random hybrid uncertain environment, in which the future returns are regarded as fuzzy random variables. Then we define (λ;γ)-expectation variance effective investment combination and discuss their efficient frontiers. Finally, a numerical analysis is investigated to expound the new model. The results show that the proposed model can provide more flexible trading strategies.

Electricity is the main driver of the economic activity in a country. In Indonesia, the fuel of electricity system is still coming from the natural resources. Batam has strategic position among other areas in Indonesia to have the highest electrification ratio as it has connected with the gas pipeline, which enables to supply gas to Batam for generating electricity and further to, meet the request by Singapore to export electricity. This thesis discussed on the forecasting risk and return to provide electricity in Batam for domestic purpose and to export to Singapore by using Efficient Frontier. Exporting electricity to Singapore will improve the electricity system in Indonesia, increase the profitability of the power plant in Indonesia, create employment in Indonesia and maximize the natural resources for domestic usage.

In A+B procurement auctions the buyer's utility is linear and the bidders' utility is assumed to be quasi-linear. If this assumption is met, then a successful auction may conclude with an efficient winning bid which maximizes both the buyer's utility and social welfare. If this assumption is not met, then an auction is either efficient and maximizes social welfare or it maximizes the buyer's utility. If the bidders are risk-averse, then a winning bid that maximizes the buyer's utility may be further improved through negotiations. It is possible to introduce side-payments which increase utility values of both the buyer and the seller.

Though electricity is getting traded as a commodity, the price of power is more volatile than any other commodity. The price of power is controlled by many unseen and random market driven factors, such as load-demand variation, attitude of market players, fuel price variation, availability of resources etc. Due to this, market participants get exposed to price-risk and their profitability gets affected. Hence since more than a decade, risk management has become an essential task for electrify market participants. In case of conventional generation, oil, coals are the major fuels. The variability of fuel price affects the price of power. In this paper, the effect of variability of fuel price on risk is analyzed. The objective of this paper is to minimize the risk associated with fuel - price variation using portfolio optimization method. This paper explains the concept of efficient frontier, a key feature of portfolio theory and its application in fuel - price risk minimization. The results are analyzed for different combinations of fuels such as coal and oil considering two approaches: Monthly Efficient Frontier and Daily Efficient Frontier. The work suggests the approach of using daily price variation to obtain optimum portfolio.

Given the variety of resources available in public clouds and locally (hybrid clouds), it can be very difficult to determine the best number and type of resources to allocate (and where) for a given activity. In order to solve this problem we first define the requested computation in terms of an Integer Linear Programming (ILP) problem and then use an efficient ILP solver to make a provisioning decision in a few milliseconds. Our approach is based on the two most important metrics for the user: cost and job execution time. Thus, based on the user's preferences we can favor solutions that optimize speed or cost or a certain combination of both (e.g. Cheapest solution that meets a certain deadline). We evaluate our approach with two classes of cloud applications: MapReduce applications, and Monte Carlo simulations. A significant advantage in our approach is that our solution has been proved optimal by the ILP solver, the set of the scheduling decisions based on our model are plotted on a time vs. Cost graph that forms a Pareto efficient frontier. This way, we can avoid the pitfalls of a naive strategy that can lead to a great increase in cost (91%) or job running time (21%) compared to optimal.

Due to transmission and other constraints, competitive electricity markets are oligopoly instead of perfectly competitive. Hence, Gencos are required to bid strategically to get more profit but the rivals complete information is not available. A strategic producer is considered who trades in day-ahead electricity market with imperfect information of rivals obtained from the historical data. Using this information, an optimization framework is developed to devise optimal bids for maximum profit with minimum risk. Conditional value at risk (CVaR) is used for the risk due to uncertain information of rival's bids. The proposed method has been tested on a six generator example and optimal solution is obtained with efficient frontier between expected losses and CVaR.

In 1950s, Markowitzs first proposed portfolio theory based on a mean-variance (MV) model to balance the risk and profit of decentralized investment. The two main inputs of MV are expected return rate and the variance of expected return rate. The expected return rate is an estimated value which is often decided by experts. Various uncertainty of stock price brings difficulties to predict return rate even for experts. MV model has its tendency to maximize the influence of errors in the input assumptions. Some scholars used fuzzy intervals to describe the return rate. However, there were still some variables decided by experts. This paper proposes a classification method to find the latent relationship between the interval return rate and the trading data of a stock and predict the interval of return rate without consulting any expert. Then this paper constructs the portfolio model based on minimax rule with interval numbers. The evaluation results show that the proposed method is reliable.

This paper presents the partial results obtained at the doctoral work titled ADAPTIVE HYBRID SYSTEM FOR THE VALUE AT RISK ESTIMATION ON PORTFOLIOS, where different AI techniques are used. This expert system tries to predict the portfolio variability with two o more assets, where the ROI and the risk rate are vital to define the efficient frontier market proposed by Markowitz.

Tradeoffs between multiple dimensions of performance are inherent in the allocation resources in many systems, particularly those with multiple stakeholders. This paper presents numerical results for the case of allocating flows in central-server closed queueing networks considering several inequity measures over many network configurations. These results show the conflict between server and customer perspectives of equity using multiple measures (server utilization, flow, wait time, and queue length). This paper first compares the effectiveness of the most equitable allocation for each measure relative to the most effective allocation for many network configurations. The complete efficient frontier is then generated using an optimization methodology. The results indicate that for low levels of server rate heterogeneity, all equity measures provide zero inequity allocations with high levels of effectiveness. However, as server rate heterogeneity increases, the total system effectiveness decreases and significant differences between the inequity measures are evident. In particular, the flow equity measure shows marked decreases in effectiveness relative to the other three measures. Further, inequity with respect to wait time, server utilization, and queue length can be eliminated with relatively small impact on total system throughput (i.e., system effectiveness). In contrast, reductions in inequity with respect to customer flow incur large decreases in total system throughput.

In recent years Exchange Traded Funds has emerged as an important investment alternative that combines both the low risk and high liquidity advantages. The construction and active management of ETFs are the central issues for the exploitation of its potential. This paper conducts the empirical studies, using the Markowitz portfolio optimization model, to construct an optimal ETF portfolio in the emerging markets. We found that the portfolio performance improves with the proposed approach against the benchmark market indexes. The performance is sensitive to the optimization criteria chosen and optimization parameters used.

The intensification of agricultural practices, in particular the growing use of fertilizers and pesticides, and the specialization and concentration of crop and livestock production, have an increasing impact on environment. This paper presents a crop planning model based on portfolio theory. The model takes into account several uncertainties as weather risks, market risks and environmental risks. Several environmental levels for the application of fertilizers/pesticides are defined. Monetary penalties for overcoming these levels, are considered. The sum of the penalties is called the environmental risk of the crop plan. The model has several constraints: budget constraints, expected return constraints and crop demand constraints. The objective map is the environmental risk. The decision variables are represented by the crop plan that is: a binary matrix that describes the crop allocations to plots and the quantities of chemical fertilizers and pesticides that are applied to crops. The goal of the model is to find the crop plans that minimize the objective map. A numerical example is considered. Simulations of the return - environmental risk efficient frontier for various lengths of historical data are analyzed.

This study presents a methodology for evolving mean-variance efficient portfolios when the agent is facing market impact costs. We use Grammatical Evolution, a form of Genetic Programming, to create portfolio strategies on an artificial market suited to simulate market impact. Classical portfolio selection as introduced by Markowitz is a well-established method to select securities based on their underlying returns and variances. This framework works well in an idealized world, where there are no market frictions and the true returns of the assets are known and normally distributed. In the real world however we face a range of problems such as transaction costs. For an active portfolio manager, transaction costs can consume a substantial amount of information value (also called a manager's alpha). One part of the transaction costs which are implicit rather than explicit are market impact costs. There has been extensive research which looks at the problem of building or liquefying a given position when facing market impact costs but it might be beneficial to look at the problem at a broader perspective where the decision which assets to include into the portfolio has not been made. We find that on the artificial market, Grammatical Evolution is able to construct portfolio strategies which considerably outperform a linearly built-up Markowitz tangency portfolio by limiting the invested amount and adjusting the portfolio weights.

A value-at-risk portfolio selection model to maximize not only the expected daily geometric return but also value-at-risk is discussed. The analytical solutions of the value-at-risk portfolio problem are derived. From the analytical results, this paper gives formulae to show the explicit relations among the following important parameters in portfolio: Value-at-risk, the expected daily geometric return, the risk probability of falling and bankruptcy and the falling rate of the asset prices. A numerical example is given to explain how to obtain the optimal portfolio and these parameters from the asset prices in the stock market.

As the amount of asset is decreased, this paper gives the characteristic of the efficient frontier under the sense of CVaR risk measurement, examines the economic implications and compares with the Mean-Variance boundary. We find that when CVaR is used as risk measurement, investors will become more stable, which is useful to risk decentralization and controlling.

The analysis on the portfolio theory doubtfully complies with shariah. Therefore, this paper presented a review to the Markowitz's Mean Variance Model (Portfolio Theory) and discussed the fundamentals underlying the model in term of shariah compliances. First, the assumptions of Markowitz's model were revised in term of compliances with shariah and the appropriate modifications were discussed that lead to the variation of efficient frontier and the characteristic of return and risk. Intriguingly, the principles of Islamic finance do agree with many conventions underlying the model. However, it was uncovered that Islamic variables such as prohibition of short selling, purification and zakat, should be integrated in the model. Lastly, the study presented empirical results on the new Islamic mean variance analysis in term of the resulting efficient frontier. In conclusion, a new revised mean-variance analysis should overcome the gap in conventional tools in measuring risk and returns and making decision on the choice of investments according to shariah.

The log-optimal or Kelly portfolio forms the basis of a theoretically appealing investment strategy. However, it is difficult to compute, and this hinders its adoption in practice. In this paper we consider an approximate Kelly portfolio based on maximizing the expected value of a quadratic approximation to log utility. We show that this semi-log approximation gives an information-theoretic justification for portfolio selection based on either the mean-variance efficient frontier or the Sharpe ratio. We further show that there is a strong connection between estimated approximate fractional Kelly portfolios and shrinkage estimators, which leads to an optimal choice of a fractional Kelly parameter. We conclude by showing that the fractional Kelly portfolio succeeds not because of reduced risk, but because of reduced estimation error. We simulate to show that this property is largely responsible for the good empirical performance of fractional Kelly strategies.

Portfolio replication problem is to optimize the portfolio such that its proportion-weighted combination is the same as the given benchmark portfolio. However, the benchmark portfolio generally opens only the return to the public but other information such as the assets included in the portfolio, the proportion-weighted combination, the rebalancing date and the investment strategies is closed to the public. In order to optimize such portfolios, we propose an optimization method based on the probabilistic model-building GA in this paper.

This overview paper reviews covariance estimation problems and related issues arising in the context of portfolio optimization. Given several assets, a portfolio optimizer seeks to allocate a fixed amount of capital among these assets so as to optimize some cost function. For example, the classical Markowitz portfolio optimization framework defines portfolio risk as the variance of the portfolio return, and seeks an allocation which minimizes the risk subject to a target expected return. If the mean return vector and the return covariance matrix for the underlying assets are known, the Markowitz problem has a closed-form solution. In practice, however, the expected returns and the covariance matrix of the returns are unknown and are therefore estimated from historical data. This introduces several problems which render the Markowitz theory impracticable in real portfolio management applications. This paper discusses these problems and reviews some of the existing literature on methods for addressing them.

We determine an opportune time to rebalance a two-asset portfolio set up using the single period Markowitz framework. This is achieved by studying and comparing the nature of portfolio evolution when two extreme rebalancing strategies are used, viz. passive or buy-and-hold and active or continuous rebalancing. We compute the rebalance time as the period during which the passive strategy generates higher expected investor utility, the Sharpe ratio. We show that the rebalance time exists only for a certain class of assets driven by their correlation coefficient.

To improve portfolio management process we suggest using profit histories of automated trading strategies instead of actual assets. Such history can be generated by simulating hundreds of automated trading strategies (robots). We developed three-level decision making system aimed to find the portfolio weights. At the first level, virtual robots trade the assets, at the second level we create virtual profit fusion agents that calculate weighted sums of the profit series created by the first level robots. At the third level, we rank the fusion agents, select a set of the best ones and construct the final portfolio. Experiments with real financial 2004–2011 years data confirm usefulness of the novel approach.