Robustness to Dependency in Portfolio Optimization Using Overlapping Marginals

Doan, Xuan Vinh; Li, Xiaobo; Natarajan, Karthik

doi:10.1287/opre.2015.1424

Cited by 37 publications

(28 citation statements)

References 56 publications

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“…To this end, we introduce a unified notation for the uncertainty quantification problems (17), (21) and (23). We denote the objective function of the unified uncertainty quantification problem by Q(ψ), where we combine all decision variables to a single vector ψ.…”

Section: Ambiguity Setmentioning

confidence: 99%

“…Ambiguity sets of special interest include the Markov ambiguity set containing all distributions with known mean and support [48], the Chebyshev ambiguity set containing all distributions with known bounds on the first and second-order moments [12,14,22,31,39,46,49,51,52], the Gauss ambiguity set containing all unimodal distributions from within the Chebyshev ambiguity set [38,41], various generalized Chebyshev ambiguity sets that specify asymmetric moments [12,13,35], higher-order moments [7,30,45] or marginal moments [17,18], the median-absolute deviation ambiguity set containing all symmetric distributions with known median and mean absolute deviation [24], the Huber ambiguity set containing all distributions with known upper bound on the expected Huber loss function [15,48], the Wasserstein ambiguity set containing all distributions that are close to the empirical distribution with respect to the Wasserstein metric [19,34,40], the KullbackLeibler divergence ambiguity set and likelihood ratio ambiguity set [10,26,27,31,47] containing all distributions that are sufficiently likely to have generated a given data set, the Hoeffding ambiguity set containing all component-wise independent distributions with a box support [3,8,10], the Bernstein ambiguity set containing all distributions from within the Hoeffding ambiguity set subject to marginal moment bounds [36], several φ-divergence-based ambiguity sets [2,…”

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confidence: 99%

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A distributionally robust perspective on uncertainty quantification and chance constrained programming

et al. 2015

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The objective of uncertainty quantification is to certify that a given physical, engineering or economic system satisfies multiple safety conditions with high probability. A more ambitious goal is to actively influence the system so as to guarantee and maintain its safety, a scenario which can be modeled through a chance constrained program. In this paper we assume that the parameters of the system are governed by an ambiguous distribution that is only known to belong to an ambiguity set characterized through generalized moment bounds and structural properties such as symmetry, unimodality or independence patterns. We delineate the watershed between tractability and intractability in ambiguity-averse uncertainty quantification and chance constrained programming. Using tools from distributionally robust optimization, we derive explicit conic reformulations for tractable problem classes and suggest efficiently computable conservative approximations for intractable ones.

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Section: Ambiguity Setmentioning

confidence: 99%

mentioning

confidence: 99%

A distributionally robust perspective on uncertainty quantification and chance constrained programming

et al. 2015

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“…For instance, Kakouris and Rustem [27] introduce an investment strategy which is robust against possible misspecification of the chosen parametric copula family. On the contrary, the more involved framework by Doan et al [12] does not need any parametric assumptions. The authors derive AV@R bounds for the Fréchet class of discrete, multivariate and overlapping marginals with finite support.…”

Section: Introductionmentioning

confidence: 98%

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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“…Quantifying the worst-case copula amounts to solving a so-called Fréchet problem. In distributionally robust optimization, Fréchet problems with discrete marginals or approximate marginal matching conditions have been studied in [13,12,43].…”

Section: Conditional Moment Informationmentioning

confidence: 99%

Distributionally robust optimization with polynomial densities: theory, models and algorithms

2019

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In distributionally robust optimization the probability distribution of the uncertain problem parameters is itself uncertain, and a fictitious adversary, e.g., nature, chooses the worst distribution from within a known ambiguity set. A common shortcoming of most existing distributionally robust optimization models is that their ambiguity sets contain pathological discrete distribution that give nature too much freedom to inflict damage. We thus introduce a new class of ambiguity sets that contain only distributions with sum-of-squares polynomial density functions of known degrees. We show that these ambiguity sets are highly expressive as they conveniently accommodate distributional information about higher-order moments, conditional probabilities, conditional moments or marginal distributions. Exploiting the theoretical properties of a measure-based hierarchy for polynomial optimization due to Lasserre [SIAM J. Optim. 21(3) (2011), pp. 864-885], we prove that certain worst-case expectation constraints are computationally tractable under these new ambiguity sets. We showcase the practical applicability of the proposed approach in the context of a stylized portfolio optimization problem and a risk aggregation problem of an insurance company.Keywords: distributionally robust optimization semidefinite programming sum-of-squares polynomials generalized eigenvalue problem AMS classification: 90C22, 90C26, 90C15

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Robustness to Dependency in Portfolio Optimization Using Overlapping Marginals

Cited by 37 publications

References 56 publications

A distributionally robust perspective on uncertainty quantification and chance constrained programming

A distributionally robust perspective on uncertainty quantification and chance constrained programming

A Review on Ambiguity in Stochastic Portfolio Optimization

Distributionally robust optimization with polynomial densities: theory, models and algorithms

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