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

R. Aboulaich; R. Ellaia; S. El Moumen

Mathematical Modelling of Natural Phenomena (2010)

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

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topAboulaich, 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

top- R. T. Rockafeller, S. Uryasev. Optimization of conditional value-at-risk. Journal of Risk, 2 (2000), No. 3, 21–42.
- S. Uryasev. Conditional value-at-risk: optimization algorithms and applications. Financial Engineering News, (2000), No. 14, 1–5.
- I. Das, J. E. Dennis. Normal boundary intersection, a new methode for generating the Pareto surface in nonlinear multicreteria optimization problems. SIAM J. Optimization, 8 (1998), No. 3, 631–657.
- C. Bonnemoy. La méthode du recuit simulé: restauration des images, reconnaissance de Surfaces. R.A.I.R.O. Automatique-Productique Informatique Industrielle, 25 (1991), No. 5, 497–517.
- H. M. Markowitz. Portfolio selection. Journal of Finance, 1 (1952), No. 7, 77–91.
- J. C. Spall. Multivariate stochastic approximation using a simultaneous perturbation gradient approximation. IEEE Transactions on Automatic Control, 37 (1992), No. 3, 332–341.
- R. T. Rockafeller, S. Uryasev. Conditional value-at-risk for general loss distributions. Journal of Banking and Finance, 26 (2002), No. 7, 1443–1471.
- 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.
- 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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