A multi-period return-risk measure portfolio optimization problem incorporating risk strategies

2010 ◽  
Author(s):  
H. Parsa ◽  
M. Jin ◽  
X. Liang
Keyword(s):  
Portfolio Optimization ◽  
Optimization Problem ◽  
Risk Measure ◽  
Portfolio Optimization Problem ◽  
Period Return

scholarly journals Scenario aggregation method for portfolio expectile optimization

2016 ◽  
Vol 33 (1-2) ◽  
Author(s):  
Edgars Jakobsons
Keyword(s):  
Portfolio Optimization ◽  
Value At Risk ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Risk Measures ◽  
Risk Measure ◽  
Conditional Value At Risk ◽  
Aggregation Method ◽  
Portfolio Optimization Problem ◽  
Scenario Aggregation

AbstractThe statistical functional expectile has recently attracted the attention of researchers in the area of risk management, because it is the only risk measure that is both coherent and elicitable. In this article, we consider the portfolio optimization problem with an expectile objective. Portfolio optimization problems corresponding to other risk measures are often solved by formulating a linear program (LP) that is based on a sample of asset returns. We derive three different LP formulations for the portfolio expectile optimization problem, which can be considered as counterparts to the LP formulations for the Conditional Value-at-Risk (CVaR) objective in the works of Rockafellar and Uryasev [

scholarly journals The Probabilistic Risk Measure VaR as Constraint in Portfolio Optimization Problem

2021 ◽  
Vol 21 (1) ◽  
pp. 19-31
Author(s):  
Todor Stoilov ◽  
Krasimira Stoilova ◽  
Miroslav Vladimirov
Keyword(s):  
Portfolio Optimization ◽  
Value At Risk ◽  
Optimization Problem ◽  
Stock Exchange ◽  
Risk Measure ◽  
Formal Analysis ◽  
Cardinality Constraints ◽  
Algebraic Form ◽  
Portfolio Problem ◽  
Portfolio Optimization Problem

Abstract The paper realizes inclusion of probabilistic measure for risk, VaR (Value at Risk), into a portfolio optimization problem. The formal analysis of the portfolio problem illustrates the evolution of the portfolio theory in sequentially inclusion of different market characteristics into the problem. They make modifications and complications of the portfolio problem by adding various constraints to consider requirements for taxes, boundaries for assets, cardinality constraints, and allocation of the investment resources. All these characteristics and parameters of the investment participate in the portfolio problem by analytical algebraic relations. The VaR definition of the portfolio risk is formalized in a probabilistic manner. The paper applies approximation of such probabilistic constraint in algebraic form. Geometrical interpretation is given for explaining the influence of the VaR constraint to the portfolio solution. Numerical simulation with data of the Bulgarian Stock Exchange illustrates the influence of the VaR constraint into the portfolio optimization problem.

MEAN-SEMIVARIANCE MODELS FOR PORTFOLIO OPTIMIZATION PROBLEM WITH MIXED UNCERTAINTY OF FUZZINESS AND RANDOMNESS

2013 ◽  
Vol 21 (supp01) ◽  
pp. 127-139 ◽  
Author(s):  
ZHONGFENG QIN ◽  
DAVID Z. W. WANG ◽  
XIANG LI
Keyword(s):  
Portfolio Optimization ◽  
Optimization Problem ◽  
Risk Measure ◽  
Fuzzy Variable ◽  
Expected Returns ◽  
Random Fuzzy Variable ◽  
Fuzzy Variables ◽  
The Mean ◽  
Security Returns ◽  
Portfolio Optimization Problem

In practice, security returns cannot be accurately predicted due to lack of historical data. Therefore, statistical methods and experts' experience are always integrated to estimate future security returns, which are hereinafter regarded as random fuzzy variables. Random fuzzy variable is a powerful tool to deal with the portfolio optimization problem including stochastic parameters with ambiguous expected returns. In this paper, we first define the semivariance of random fuzzy variable and prove its several properties. By considering the semivariance as a risk measure, we establish the mean-semivariance models for portfolio optimization problem with random fuzzy returns. We design a hybrid algorithm with random fuzzy simulation to solve the proposed models in general cases. Finally, we present a numerical example and compare the results to illustrate the mean-semivariance model and the effectiveness of the algorithm.

scholarly journals Modeling and Optimizing the Multi-Objective Portfolio Optimization Problem with Trapezoidal Fuzzy Parameters

2021 ◽  
Vol 26 (2) ◽  
pp. 36
Author(s):  
Alejandro Estrada-Padilla ◽  
Daniela Lopez-Garcia ◽  
Claudia Gómez-Santillán ◽  
Héctor Joaquín Fraire-Huacuja ◽  
Laura Cruz-Reyes ◽  
...  
Keyword(s):  
Steady State ◽  
Portfolio Optimization ◽  
Optimization Problem ◽  
Solution Process ◽  
Density Estimator ◽  
Nsga Ii ◽  
Spatial Spread ◽  
Multi Objective ◽  
Significant Difference ◽  
Portfolio Optimization Problem

A common issue in the Multi-Objective Portfolio Optimization Problem (MOPOP) is the presence of uncertainty that affects individual decisions, e.g., variations on resources or benefits of projects. Fuzzy numbers are successful in dealing with imprecise numerical quantities, and they found numerous applications in optimization. However, so far, they have not been used to tackle uncertainty in MOPOP. Hence, this work proposes to tackle MOPOP’s uncertainty with a new optimization model based on fuzzy trapezoidal parameters. Additionally, it proposes three novel steady-state algorithms as the model’s solution process. One approach integrates the Fuzzy Adaptive Multi-objective Evolutionary (FAME) methodology; the other two apply the Non-Dominated Genetic Algorithm (NSGA-II) methodology. One steady-state algorithm uses the Spatial Spread Deviation as a density estimator to improve the Pareto fronts’ distribution. This research work’s final contribution is developing a new defuzzification mapping that allows measuring algorithms’ performance using widely known metrics. The results show a significant difference in performance favoring the proposed steady-state algorithm based on the FAME methodology.

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