Integrated Chance Constraints: Reduced Forms and an Algorithm

Haneveld, Willem K. Klein; Vlerk, Maarten H. van der

doi:10.1007/s10287-005-0007-3

Cited by 92 publications

(58 citation statements)

References 12 publications

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“…In [16], Klein Haneveld and van der Vlerk propose a cutting plane algorithm for solving problems with integrated chance constraints and demonstrate its computational efficiency. Due to (6), this approach can also be used for problems with second-order stochastic dominance constraints, as has been observed in [8].…”

Section: Review Of Existing Resultsmentioning

confidence: 99%

“…Independently, Gabor and Ruszczyński [26] proposed a primal cutting plane method and a dual column generation method for optimization problems with second-order stochastic dominance constraints, and the primal method is shown to be computationally efficient. In the case of finite distributions, the primal cutting plane method is equivalent to the cutting plane method used for integrated chance constraints in [16].…”

Section: Review Of Existing Resultsmentioning

confidence: 99%

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New Formulations for Optimization under Stochastic Dominance Constraints

Luedtke¹

2008

SIAM J. Optim.

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Stochastic dominance constraints allow a decision-maker to manage risk in an optimization setting by requiring their decision to yield a random outcome which stochastically dominates a reference random outcome. We present new integer and linear programming formulations for optimization under first and second-order stochastic dominance constraints, respectively. These formulations are more compact than existing formulations, and relaxing integrality in the first-order formulation yields a second-order formulation, demonstrating the tightness of this formulation. We also present a specialized branching strategy and heuristics which can be used with the new first-order formulation. Computational tests illustrate the potential benefits of the new formulations.

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Section: Review Of Existing Resultsmentioning

confidence: 99%

Section: Review Of Existing Resultsmentioning

confidence: 99%

New Formulations for Optimization under Stochastic Dominance Constraints

Luedtke¹

2008

SIAM J. Optim.

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“…This method is an extension of the cutting-plane method developed by Haneveld and Vlerk [16] for integrated chance constraints (ICC). In what follows, we consider a modification of the procedure where a cut is constructed.…”

Section: Modified Cutting Plane Algorithmmentioning

confidence: 99%

“…This cutting plane method differs from those in the literature [24] in that it applies to the maximum of the constraint functions rather than each constraint function. Moreover, our modified cutting plane method uses the cutting plane representation proposed in [16], so it differ from the methods proposed in [10,14]. The idea of applying the cutting-plane method to the maximum of the constraint functions is similar to the idea in algorithm proposed by Fábián et al [8].…”

Section: Introductionmentioning

confidence: 99%

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

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“…Fishburn (1964), Föllmer and Schied (2004), Dentcheva and Ruszczyński (2003). Considerable effort has been put in efficient algorithms that can cope with the huge amount of restrictions in the corresponding LP-problems, in particular by means of cutting-plane methods, see Klein Haneveld and van der Vlerk (2006), Künzi-Bay and Mayer (2006), Rudolf and Ruszczyński (2008), Luedtke (2008), Fábián et al (2009).…”

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confidence: 99%

An algorithm for sequential tail value at risk for path-independent payoffs in a binomial tree

Roorda

2010

Ann Oper Res

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We present an algorithm that determines Sequential Tail Value at Risk (STVaR) for path-independent payoffs in a binomial tree. STVaR is a dynamic version of Tail-Valueat-Risk (TVaR) characterized by the property that risk levels at any moment must be in the range of risk levels later on. The algorithm consists of a finite sequence of backward recursions that is guaranteed to arrive at the solution of the corresponding dynamic optimization problem. The algorithm makes concrete how STVaR differs from TVaR over the remaining horizon, and from recursive TVaR, which amounts to Dynamic Programming. Algorithmic aspects are compared with the cutting-plane method. Time consistency and comonotonicity properties are illustrated by applying the algorithm on elementary examples.

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Integrated Chance Constraints: Reduced Forms and an Algorithm

Abstract: Chance constraints, Simple recourse, Algorithm, 90C15,

Cited by 92 publications

References 12 publications

New Formulations for Optimization under Stochastic Dominance Constraints

New Formulations for Optimization under Stochastic Dominance Constraints

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

An algorithm for sequential tail value at risk for path-independent payoffs in a binomial tree

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