Numerical methods for stochastic programs with second order dominance constraints with applications to portfolio optimization

Meskarian, Rudabeh; Xu, Huifu; Fliege, Jörg

doi:10.1016/j.ejor.2011.07.044

Cited by 22 publications

(15 citation statements)

References 24 publications

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“…As a relation of model (11), model (12) has a larger set of feasible solutions and subsequently its optimal value gives a lower bound for model. Besides, the relaxed model is more likely to satisfy the Slater condition which is closely related to numerical stability [9].…”

Section: The Second Order Stochastic Dominance Modelmentioning

confidence: 99%

“…the probability distribution of ξ [9]. The constraints of model (7) are based on the definition of second order stochastic dominance, Fábián [7] and Ogryczak [22] prove that the constraint g(x, ξ) 2 g(y, ξ) is equivalent to the following two inequalities:…”

Section: The Second Order Stochastic Dominance Modelmentioning

confidence: 99%

“…Combined with the constraint (9), the model (7) can be formulated as a stochastic semi-infinite programming problem [3,9] :…”

Section: The Second Order Stochastic Dominance Modelmentioning

confidence: 99%

“…Short-selling is the sale of a security that is not owned by the seller, or the seller has borrowed. If the short-selling is allowed and investors do not want to invest very small amounts in an asset, the upper and lower bounds on the fraction of capital invested in each assets are set to 2 and −1 [9]:…”

Section: Portfolio Optimization Modelmentioning

confidence: 99%

“…However, the number of variables in the model depends on the number of investable assets, which increases the pressure of calculation. Meskarian, Xu and Fliege [9] penalize SSD constraints to the objective under Slater's constraint qualification and apply the SA method and LF method to solve the penalized problem. Hu [10] apply the Sample Average Approximation method into SSD model, which introduces new variables into the model.…”

Section: Introductionmentioning

confidence: 99%

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Biogeography-Based Optimization of the Portfolio Optimization Problem with Second Order Stochastic Dominance Constraints

2017

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Abstract:The portfolio optimization problem is the central problem of modern economics and decision theory; there is the Mean-Variance Model and Stochastic Dominance Model for solving this problem. In this paper, based on the second order stochastic dominance constraints, we propose the improved biogeography-based optimization algorithm to optimize the portfolio, which we called εBBO. In order to test the computing power of εBBO, we carry out two numerical experiments in several kinds of constraints. In experiment 1, comparing the Stochastic Approximation (SA) method with the Level Function (LF) algorithm and Genetic Algorithm (GA), we get a similar optimal solution by εBBO in [0, 0.6] and [0, 1] constraints with the return of 1.174% and 1.178%. In [−1, 2] constraint, we get the optimal return of 1.3043% by εBBO, while the return of SA and LF is 1.23% and 1.26%. In experiment 2, we get the optimal return of 0.1325% and 0.3197% by εBBO in [0, 0.1] and [−0.05, 0.15] constraints. As a comparison, the return of FTSE100 Index portfolio is 0.0937%. The results prove that εBBO algorithm has great potential in the field of financial decision-making, it also shows that εBBO algorithm has a better performance in optimization problem.

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Section: The Second Order Stochastic Dominance Modelmentioning

confidence: 99%

Section: The Second Order Stochastic Dominance Modelmentioning

confidence: 99%

“…Combined with the constraint (9), the model (7) can be formulated as a stochastic semi-infinite programming problem [3,9] :…”

Section: The Second Order Stochastic Dominance Modelmentioning

confidence: 99%

Section: Portfolio Optimization Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Biogeography-Based Optimization of the Portfolio Optimization Problem with Second Order Stochastic Dominance Constraints

2017

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On relations between chance constrained and penalty function problems under discrete distributions

Branda

2013

Math Meth Oper Res

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Stochastic Programming with Multivariate Second Order Stochastic Dominance Constraints with Applications in Portfolio Optimization

Meskarian

Fliege

2014

Appl Math Optim

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In this paper we study optimization problems with multivariate stochastic dominance constraints where the underlying functions are not necessarily linear. These problems are important in multicriterion decision making, since each component of vectors can be interpreted as the uncertain outcome of a given criterion. We propose a penalization scheme for the multivariate second order stochastic dominance constraints. We solve the penalized problem by the level function methods, and a modified cutting plane method and compare them to the cutting surface method proposed in the literature. The proposed numerical schemes are applied to a generic budget allocation problem and a real world portfolio optimization problem.AMS Classification: 90C15 and 90C90

show abstract

Numerical methods for stochastic programs with second order dominance constraints with applications to portfolio optimization

Cited by 22 publications

References 24 publications

Biogeography-Based Optimization of the Portfolio Optimization Problem with Second Order Stochastic Dominance Constraints

Biogeography-Based Optimization of the Portfolio Optimization Problem with Second Order Stochastic Dominance Constraints

On relations between chance constrained and penalty function problems under discrete distributions

Stochastic Programming with Multivariate Second Order Stochastic Dominance Constraints with Applications in Portfolio Optimization

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