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 An Improvement of Stochastic Gradient Descent Approach for Mean-Variance Portfolio Optimization Problem

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Stephanie S. W. Su ◽  
Sie Long Kek
Keyword(s):  
Portfolio Optimization ◽  
Standard Error ◽  
Gradient Descent ◽  
Optimization Problem ◽  
Stochastic Gradient Descent ◽  
Moment Estimation ◽  
The Mean ◽  
Portfolio Optimization Problem ◽  
Mean Variance Portfolio ◽  
Mean Variance

In this paper, the current variant technique of the stochastic gradient descent (SGD) approach, namely, the adaptive moment estimation (Adam) approach, is improved by adding the standard error in the updating rule. The aim is to fasten the convergence rate of the Adam algorithm. This improvement is termed as Adam with standard error (AdamSE) algorithm. On the other hand, the mean-variance portfolio optimization model is formulated from the historical data of the rate of return of the S&P 500 stock, 10-year Treasury bond, and money market. The application of SGD, Adam, adaptive moment estimation with maximum (AdaMax), Nesterov-accelerated adaptive moment estimation (Nadam), AMSGrad, and AdamSE algorithms to solve the mean-variance portfolio optimization problem is further investigated. During the calculation procedure, the iterative solution converges to the optimal portfolio solution. It is noticed that the AdamSE algorithm has the smallest iteration number. The results show that the rate of convergence of the Adam algorithm is significantly enhanced by using the AdamSE algorithm. In conclusion, the efficiency of the improved Adam algorithm using the standard error has been expressed. Furthermore, the applicability of SGD, Adam, AdaMax, Nadam, AMSGrad, and AdamSE algorithms in solving the mean-variance portfolio optimization problem is validated.

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.

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