# The Mean-Variance-CVaR model for Portfolio Optimization Modeling using a Multi-Objective Approach Based on a Hybrid Method

• Volume: 5, Issue: 7, page 103-108
• ISSN: 0973-5348

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## Abstract

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In this paper we present a new hybrid method, called SASP method. We propose the hybridization of two methods, the simulated annealing (SA), which belong to the class of global optimization based on the principles of thermodynamics, and the descent method were we estimate the gradient using the simultaneous perturbation. This hybrid method gives better results. We use the Normal Boundary Intersection approach (NBI) based on the SASP method to solve a portfolio optimization problem. Such problem is a multi-objective optimization problem, in order to solve this problem we use three statistical quantities: the expected value, the variance and the Conditional Value-at-Risk (CVaR). The purpose of this work is to find the efficient boundary of the considered multi-objective problem using the NBI method based on the SASP method

## How to cite

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Aboulaich, R., Ellaia, R., and El Moumen, S.. Taik, A., ed. "The Mean-Variance-CVaR model for Portfolio Optimization Modeling using a Multi-Objective Approach Based on a Hybrid Method." Mathematical Modelling of Natural Phenomena 5.7 (2010): 103-108. <http://eudml.org/doc/197690>.

@article{Aboulaich2010,
abstract = {In this paper we present a new hybrid method, called SASP method. We propose the hybridization of two methods, the simulated annealing (SA), which belong to the class of global optimization based on the principles of thermodynamics, and the descent method were we estimate the gradient using the simultaneous perturbation. This hybrid method gives better results. We use the Normal Boundary Intersection approach (NBI) based on the SASP method to solve a portfolio optimization problem. Such problem is a multi-objective optimization problem, in order to solve this problem we use three statistical quantities: the expected value, the variance and the Conditional Value-at-Risk (CVaR). The purpose of this work is to find the efficient boundary of the considered multi-objective problem using the NBI method based on the SASP method},
author = {Aboulaich, R., Ellaia, R., El Moumen, S.},
editor = {Taik, A.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {CVaR; multi-objective optimization; NBI method; hybrid method SASP; simultaneous perturbation; simulated annealing},
language = {eng},
month = {8},
number = {7},
pages = {103-108},
publisher = {EDP Sciences},
title = {The Mean-Variance-CVaR model for Portfolio Optimization Modeling using a Multi-Objective Approach Based on a Hybrid Method},
url = {http://eudml.org/doc/197690},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Aboulaich, R.
AU - Ellaia, R.
AU - El Moumen, S.
AU - Taik, A.
TI - The Mean-Variance-CVaR model for Portfolio Optimization Modeling using a Multi-Objective Approach Based on a Hybrid Method
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/8//
PB - EDP Sciences
VL - 5
IS - 7
SP - 103
EP - 108
AB - In this paper we present a new hybrid method, called SASP method. We propose the hybridization of two methods, the simulated annealing (SA), which belong to the class of global optimization based on the principles of thermodynamics, and the descent method were we estimate the gradient using the simultaneous perturbation. This hybrid method gives better results. We use the Normal Boundary Intersection approach (NBI) based on the SASP method to solve a portfolio optimization problem. Such problem is a multi-objective optimization problem, in order to solve this problem we use three statistical quantities: the expected value, the variance and the Conditional Value-at-Risk (CVaR). The purpose of this work is to find the efficient boundary of the considered multi-objective problem using the NBI method based on the SASP method
LA - eng
KW - CVaR; multi-objective optimization; NBI method; hybrid method SASP; simultaneous perturbation; simulated annealing
UR - http://eudml.org/doc/197690
ER -

## References

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5. H. M. Markowitz. Portfolio selection. Journal of Finance, 1 (1952), No. 7, 77–91.
6. J. C. Spall. Multivariate stochastic approximation using a simultaneous perturbation gradient approximation. IEEE Transactions on Automatic Control, 37 (1992), No. 3, 332–341.
7. R. T. Rockafeller, S. Uryasev. Conditional value-at-risk for general loss distributions. Journal of Banking and Finance, 26 (2002), No. 7, 1443–1471.
8. Q. Yuan, Z. He, H. Leng. A hybrid genetic algorithm for a class of global optimization problems with box constraints. Applied Mathematics and Computation, 197 (2008), No. 2, 924–929.
9. I. G. Tsoulos. Modifications of real code genetic algorithm for global optimization. Applied Mathematics and Computation, 203 (2008), No. 2, 598–607.

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