A distributionally robust perspective on uncertainty quantification and chance constrained programming

Hanasusanto, Grani A.; Roitch, Vladimir; Kühn, Daniel; Wiesemann, Wolfram

doi:10.1007/s10107-015-0896-z

Cited by 146 publications

(100 citation statements)

References 47 publications

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“…Similar results have been proved in [25]. More recently, Hanasusanto et al [20] investigate tractability of a richer class of ambiguity sets defined through moment conditions and structural information such as symmetry, unimodality, and independence patterns for MPDRCC.…”

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confidence: 70%

Convergence Analysis for Mathematical Programs with Distributionally Robust Chance Constraint

Guo¹,

Xu²,

Zhang³

2017

SIAM J. Optim.

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Abstract. Convergence analysis for optimization problems with chance constraints concerns impact of variation of probability measure in the chance constraints on the optimal value and the optimal solutions and research on this topic has been well documented in the literature of stochastic programming. In this paper, we extend such analysis to optimization problems with distributionally robust chance constraints where the true probability distribution is unknown, but it is possible to construct an ambiguity set of probability distributions and the chance constraint is based on the most conservative selection of probability distribution from the ambiguity set. The convergence analysis focuses on impact of the variation of the ambiguity set on the optimal value and the optimal solutions. We start by deriving general convergence results under abstract conditions such as continuity of the robust probability function and uniform convergence of the robust probability functions and followed with detailed analysis of these conditions. Two sufficient conditions have been derived with one applicable to both continuous and discrete probability distribution and the other to continuous distribution. Case studies are carried out for ambiguity sets being constructed through moments and samples.

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confidence: 70%

Convergence Analysis for Mathematical Programs with Distributionally Robust Chance Constraint

Guo¹,

Xu²,

Zhang³

2017

SIAM J. Optim.

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“…in [10,13,31]. This approach can be extended to ambiguity sets which are characterized, additionally to the moment bounds, by constraints on structural properties auch as symmetry, unimodality or independence patterns, see Hanasusanto et al [24]. Another field of research deals with sample average approximations, where ambiguity sets appear as confidence regions, see e.g.…”

Section: Ambiguity Setsmentioning

confidence: 99%

A Review on Ambiguity in Stochastic Portfolio Optimization

Pflug

Pohl

2017

Set-Valued Var. Anal

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In mean-risk portfolio optimization, it is typically assumed that the assets follow a known distribution P 0 , which is estimated from observed data. Aiming at an investment strategy which is robust against possible misspecification of P 0 , the portfolio selection problem is solved with respect to the worst-case distribution within a Wasserstein-neighborhood of P 0 . We review tractable formulations of the portfolio selection problem under model ambiguity, as it is called in the literature. For instance, it is known that high model ambiguity leads to equally-weighted portfolio diversification. However, it often happens that the marginal distributions of the assets can be estimated with high accuracy, whereas the dependence structure between the assets remains ambiguous. This leads to the problem of portfolio selection under dependence uncertainty. We show that in this case portfolio concentration becomes optimal as the uncertainty with respect to the estimated dependence structure increases. Hence, distributionally robust portfolio optimization can have two very distinct implications: Diversification on the one hand and concentration on the other hand.

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“…For a broad overview of types of ambiguity sets we refer the reader to Postek et al (2016) and Hanasusanto et al (2015). Among these alternative setups, there are some cases for which exact reformulations are possible.…”

Section: Alternative Ambiguity Setupsmentioning

confidence: 99%

Robust Optimization with Ambiguous Stochastic Constraints Under Mean and Dispersion Information

Postek

Ben‐Tal

Hertog

et al. 2018

Operations Research

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Abstract. In this paper we consider ambiguous stochastic constraints under partial information consisting of means and dispersion measures of the underlying random parameters. Whereas the past literature used the variance as the dispersion measure, here we use the mean absolute deviation from the mean (MAD). This makes it possible to use the 1972 result of Ben-Tal and Hochman (BH) in which tight upper and lower bounds on the expectation of a convex function of a random variable are given. First, we use these results to treat ambiguous expected feasibility constraints to obtain exact reformulations for both functions that are convex and concave in the components of the random variable. This approach requires, however, the independence of the random variables and, moreover, may lead to an exponential number of terms in the resulting robust counterparts. We then show how upper bounds can be constructed that alleviate the independence restriction, and require only a linear number of terms, by exploiting models in which random variables are linearly aggregated. Moreover, using the BH bounds we derive three new safe tractable approximations of chance constraints of increasing computational complexity and quality. In a numerical study, we demonstrate the efficiency of our methods in solving stochastic optimization problems under mean-MAD ambiguity.

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A distributionally robust perspective on uncertainty quantification and chance constrained programming

Cited by 146 publications

References 47 publications

Convergence Analysis for Mathematical Programs with Distributionally Robust Chance Constraint

Convergence Analysis for Mathematical Programs with Distributionally Robust Chance Constraint

A Review on Ambiguity in Stochastic Portfolio Optimization

Robust Optimization with Ambiguous Stochastic Constraints Under Mean and Dispersion Information

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