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### Fuzzy Portfolio Selection Problem with Different Borrowing and Lending Rates

Wei Chen, Yiping Yang, Hui Ma
2011 Mathematical Problems in Engineering
In this paper, the returns of each assets are assumed to be fuzzy variables, then following the mean-variance approach, a new possibilistic portfolio selection model with different interest rates for borrowing  ...  and lending is proposed, in which the possibilistic semiabsolute deviation of the return is used to measure investment risk.  ...  Therefore, the possibilistic semi-absolute deviation can be defined as ω P M max{0, M P − P } . 2.13 Based on the Theorem 2.1, the interval-valued possibilistic semi-absolute deviation is represented as  ...

### The mean-absolute deviation portfolio selection problem with interval-valued returns

Shiang-Tai Liu
2011 Journal of Computational and Applied Mathematics
According to the concept of the mean-absolute deviation function, we construct a pair of two-level mathematical programming models to calculate the lower and upper bounds of the investment return of the  ...  Since the parameters are interval valued, the gain of returns is interval valued as well.  ...  Acknowledgements This research was supported by the National Science Council of the Republic of China under Contract No. NSC96-2410-H-238-004-MY2. The author is indebted to Editor M.J.  ...

### Robustness-based portfolio optimization under epistemic uncertainty

2018 Journal of Industrial Engineering International
return and risk.  ...  information) arising from interval data.  ...  In the future, the proposed model can be compared with the linear robust risk estimator such as Mean Absolute Deviation and Median Absolute Deviation.  ...

### Optimization of Fuzzy Portfolio Considering Stock Returns and Downside Risk

2016 International Journal of Science and Research (IJSR)
We assume that the rates of returns on securities are approximated as LR-fuzzy numbers of the same shape, and that the expected return and risk are evaluated by interval-valued means.  ...  We establish the relationship between those mean-interval definitions for a given fuzzy portfolio by using suitable ordering relations. And then we compare those with a given not fuzzy portfolio one.  ...  Taking the uncertainty of returns on assets in a financial market as trapezoidal LR-fuzzy numbers, we generalize the mean semi-absolute deviation using both interval-valued probabilistic and possibilistic  ...

### Fuzzy portfolio optimization under downside risk measures

Enriqueta Vercher, José D. Bermúdez, José Vicente Segura
2007 Fuzzy sets and systems (Print)
We assume that the rates of returns on securities are approximated as LR-fuzzy numbers of the same shape, and that the expected return and risk are evaluated by interval-valued means.  ...  Finally, we formulate the portfolio selection problem as a linear program when the returns on the assets are of trapezoidal form.  ...  In general portfolio selection problems a probability distribution of the return on the assets is assumed to be known, the return is quantified by means of its expected value and the variance of the portfolio  ...

### Minimization of Portfolio Risk using Three Different Methods (A Comparative Study)

Hegazy Zaher, Nisren Hassanen Mohamed
2015 International Journal of Computer Applications
A comparison between the three proposed methods is conducted using three different measures of error (the Mean-Variance (MV), Mean-Absolute Deviation (MAD), Conditional Value-at-Risk (CVaR)).  ...  Portfolio risk plays an important role in stock market decisions. This paper considers an alternative idea which is to compute the risk assuming fixed return.  ...  This model calculates the portfolio to minimizing MAD subject to a lower bound on the return.  ...

### A class of linear interval programming problems and its application to portfolio selection

K.K. Lai, S.Y. Wang, J.P. Xu, S.S. Zhu, Y. Fang
2002 IEEE transactions on fuzzy systems
Considering the uncertain returns of assets in capital markets as intervals, we propose a model for portfolio selection based on the semiabsolute deviation measure of risk, which can be transformed to  ...  The noninferior solutions to such problems are defined based on two order relations between intervals, and can be found by solving a parametric linear programming problem.  ...  Konno and Yamazika  used the absolute deviation risk function to replace the risk function in Markowitz's mean-variance model and formulated a mean absolute deviation portfolio optimization model  ...

### THE PROPER USE OF RISK MEASURES IN PORTFOLIO THEORY

SERGIO ORTOBELLI, SVETLOZAR T. RACHEV, STOYAN STOYANOV, FRANK J. FABOZZI, ALMIRA BIGLOVA
2005 International Journal of Theoretical and Applied Finance
Finally, we propose an empirical comparison among three different portfolio choice models which depend on the mean, on a risk measure, and on a skewness parameter.  ...  Thus, we assess and value the impact on the investor's preferences of three different risk measures even considering some derivative assets among the possible choices.  ...  ). expected utility of the future wealth y W has a mean greater than y µ and the expected utility depends only on the mean and the risk measure p.  ...

### A Simple Model of Robust Portfolio Selection

Marco Taboga
2004 Social Science Research Network
We propose a single-period portfolio selection model which allows the decision maker to easily deal with uncertainty about the distribution of asset returns.  ...  A particular speci...cation of preferences allows us to solve the portfolio selection problem and obtain a simple closed-form expression for the portfolio weights, which lends itself to a straightforward  ...  are the mean and the variance of the gross return on asset i.  ...

### Simulating the market coefficient of relative risk aversion

2014 Cogent Economics & Finance
The following parameters are varied: the riskless return, the market standard deviation, the market stock premium, and the skewness and the kurtosis of the risky return.  ...  Abstract: In this paper, expected utility, defined by a Taylor series expansion around expected wealth, is maximized.  ...  In the CAPM, this average risk is the market systematic risk, and the average return is the return on an average-risk capital asset.  ...

### Portfolio Optimization under Cardinality Constraints: A Comparative Study

Henri Claver Jimbo, Isidore Seraphin Ngongo, Nicolas Gabriel Andjiga, Takeru Suzuki, Charles Awona Onana
2017 Open Journal of Statistics
In portfolio optimization problem, the cardinality constraint allows one to invest in K N ≤ assets out of a universe of N assets for a prespecified value of K.  ...  It is generally agreed that choosing a "small" value of K forces the implementation of diversification in small portfolios. However, the question of how small must be K has remained unanswered.  ...  This approach will then challenge the Markowitz belief that the only optimal portfolio is the one with higher expected mean portfolio value and smaller risk or standard deviation.  ...

### Optimal Hedge Fund Allocation with Asymmetric Preferences and Distributions

Ivilina Popova, Elmira Popova, David Morton, Jot Yau
2006 Social Science Research Network
By employing these two bounding ideas together, a confidence interval on the optimality gap (the difference between the optimal value of the objective function, z * , and the value for a given solution  ...  Asset 1 has a monthly mean of 1% and a monthly standard deviation of 4%; Asset 2 has the same mean and standard deviation, additionally Asset 2 has a negative skewness and high kurtosis.  ...

### A Bayesian approach to diagnosis of asset pricing models

Michael Stutzer
1995 Journal of Econometrics
A large literature has arisen which exploits a particular portfolio on the mean-variance frontier, determining a minimum variance bound on the set of stochastic discount factors (state price to probability  ...  Furthermore, the information bound is determined by a portfolio which maximizes expected CARA utility.  ...  As expected, there are more negative values when the variance bound is higher. Maximum SDF elements are larger in absolute value than minimum elements.  ...

### Robust Portfolio Selection Problems: A Comprehensive Review [article]

Alireza Ghahtarani, Ahmed Saif, Alireza Ghasemi
2022 arXiv   pre-print
Several open questions and potential future research directions are identified.  ...  In this paper, we provide a comprehensive review of recent advances in robust portfolio selection problems and their extensions, from both operational research and financial perspectives.  ...  Benati & Conde (2021) proposed a model that minimizes the maximum regret on the expected returns while the conditional value-at-risk is bounded under different scenario settings.  ...

### Chance-constrained multiperiod mean absolute deviation uncertain portfolio selection

Peng Zhang
2017 Journal of Industrial and Management Optimization
In proposed model, the return rate of asset is quantified by uncertain expected value and the risk is characterized by uncertain absolute deviation.  ...  The chance constraints are that the uncertain expected return of the portfolio selection is bigger than the preset return of investors under the given confidence level.  ...  The risk on the return rate of portfolio at each period is quantified by the uncertain absolute deviation.  ...
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