Fetching the paper…
Reading the bibliography…
We introduce a universal framework for mean-covariance robust risk measurement and portfolio optimization.
A Treatise on Probability
J. M. Keynes · 1921
Earlier work this paper cites.
Risk, Uncertainty and Profit
F. H. Knight · 1921
Earlier work this paper cites.
Portfolio selection
H. Markowitz · 1952
Earlier work this paper cites.
Remarks on a multivariate transformation
M. Rosenblatt · 1952
Earlier work this paper cites.
Safety first and the holding of assets
A. Roy · 1952
Earlier work this paper cites.
On general minimax theorems
M. Sion · 1958
Earlier work this paper cites.
Risk, ambiguity and the Savage axioms
D. Ellsberg · 1961
Earlier work this paper cites.
Topological Spaces: Including a Treatment of Multi-Valued Functions, Vector Spaces, and Convexity
C. Berge · 1963
Earlier work this paper cites.
Robust estimation of a location parameter
P. J. Huber · 1964
Earlier work this paper cites.
Lifetime portfolio selection under uncertainty: The continuous-time case
R. C. Merton · 1969
Earlier work this paper cites.
A bound on tail probabilities for quadratic forms in independent random variables
D. L. Hanson and F. T. Wright · 1971
Earlier work this paper cites.
Robust M-estimators of multivariate location and scatter
R. A. Maronna · 1976
Earlier work this paper cites.
On the theory of elliptically contoured distributions
S. Cambanis, S. Huang, and G. Simons · 1981
Earlier work this paper cites.
Robust Statistics
P. J. Huber · 1981
Earlier work this paper cites.
The Fréchet distance between multivariate normal distributions
D. Dowson and B. Landau · 1982
Earlier work this paper cites.
The distance between two random vectors with given dispersion matrices
I. Olkin and F. Pukelsheim · 1982
Earlier work this paper cites.
Convexity of measures in certain convex cones in vector space σ \sigma -algebras
C. Borell · 1983
Earlier work this paper cites.
Problem Complexity and Method Efficiency in Optimization
A. S. Nemirovskij and D. B. Yudin · 1983
Earlier work this paper cites.
A class of Wasserstein metrics for probability distributions
C. Givens and R. Shortt · 1984
Earlier work this paper cites.
On the optimal mapping of distributions
M. Knott and C. S. Smith · 1984
Earlier work this paper cites.
Robust regression by means of S-estimators
P. Rousseeuw and V. Yohai · 1984
Earlier work this paper cites.
Least median of squares regression
P. J. Rousseeuw · 1984
Earlier work this paper cites.
Convex Statistical Distances
F. Liese and I. Vajda · 1987
Earlier work this paper cites.
The dual theory of choice under risk
M. E. Yaari · 1987
Earlier work this paper cites.
Unimodality, Convexity, and Applications
S. Dharmadhikari and K. Joag-Dev · 1988
Earlier work this paper cites.
Maxmin expected utility with non-unique prior
I. Gilboa and D. Schmeidler · 1989
Earlier work this paper cites.
On the relation between S-estimators and M-estimators of multivariate location and covariance
H. P. Lopuhaä · 1989
Earlier work this paper cites.
The Markowitz optimization enigma: Is ‘optimized’ optimal?
R. O. Michaud · 1989
Earlier work this paper cites.
On a formula for the L 2 {L}^{2} Wasserstein metric between measures on Euclidean and Hilbert spaces
M. Gelbrich · 1990
Earlier work this paper cites.
Functional Analysis
F. Riesz and B. Sz.-Nagy · 1990
Earlier work this paper cites.
On the sensitivity of mean-variance-efficient portfolios to changes in asset means: Some analytical and computational results
M. J. Best and R. R. Grauer · 1991
Earlier work this paper cites.
When will mean-variance efficient portfolios be well diversified?
R. C. Green and B. Hollifield · 1992
Earlier work this paper cites.
Perturbation bounds for matrix square roots and Pythagorean sums
B. A. Schmitt · 1992
Earlier work this paper cites.
The effect of errors in means, variances and covariances on optimal portfolio choice
V. K. Chopra and W. T. Ziemba · 1993
Earlier work this paper cites.
Optimal coupling of multivariate distributions and stochastic processes
J. A. Cuesta-Albertos, L. Rüschendorf, and A. Tuero-Diaz · 1993
Earlier work this paper cites.
On lower bounds for the L 2 {L}^{2} -Wasserstein metric in a Hilbert space
J. A. Cuesta-Albertos, C. Matrán-Bea, and A. Tuero-Diaz · 1996
Earlier work this paper cites.
Value at Risk: The New Benchmark for Managing Financial Risk
P. Jorion · 1996
Earlier work this paper cites.
RiskMetrics TM \phantom{}{}^{\text{\tiny{TM}}} —Technical Document
J. Longerstaey and M. Spencer · 1996
Earlier work this paper cites.
An overview of value at risk
D. Duffie and J. Pan · 1997
Earlier work this paper cites.
Investment Science
D. G. Luenberger · 1997
Earlier work this paper cites.
On the calculation of a robust S-estimator of a covariance matrix
N. Campbell, H. P. Lopuhaä, and P. J. Rousseeuw · 1998
Earlier work this paper cites.
Applications of second-order cone programming
M. S. Lobo, L. Vandenberghe, S. Boyd, and H. Lebret · 1998
Cited alongside, same era.
Coherent measures of risk
P. Artzner, F. Delbaen, J.-M. Eber, and D. Heath · 1999
Cited alongside, same era.
A fast algorithm for the minimum covariance determinant estimator
P. J. Rousseeuw and K. V. Driessen · 1999
Cited alongside, same era.
Optimization of conditional value-at-risk
R. T. Rockafellar and S. Uryasev · 2000
Cited alongside, same era.
Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications
A. Ben-Tal and A. Nemirovski · 2001
Cited alongside, same era.
On law invariant coherent risk measures
S. Kusuoka · 2001
Cited alongside, same era.
On Kusuoka representation of law invariant risk measures
A. Shapiro · 2013
Later among the works it cites.
Distributionally robust convex optimization
W. Wiesemann, D. Kuhn, and M. Sim · 2014
Later among the works it cites.
Robustifying convex risk measures for linear portfolios: A nonparametric approach
D. Wozabal · 2014
Later among the works it cites.
Deriving robust counterparts of nonlinear uncertain inequalities
A. Ben-Tal, D. Den Hertog, and J. P. Vial · 2015
Later among the works it cites.
Robustness to dependency in portfolio optimization using overlapping marginals
X. V. Doan, X. Li, and K. Natarajan · 2015
Later among the works it cites.
On the rate of convergence in Wasserstein distance of the empirical measure
N. Fournier and A. Guillin · 2015
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Spectral measures of risk: A coherent representation of subjective risk aversion
C. Acerbi · 2002
Cited alongside, same era.
The Cornish-Fisher-Expansion in the context of Delta-Gamma-Normal approximations
S. R. Jaschke · 2002
Cited alongside, same era.
Deviation measures in risk analysis and optimization
R. T. Rockafellar, S. P. Uryasev, and M. Zabarankin · 2002
Cited alongside, same era.
Worst-case value-at-risk and robust portfolio optimization: A conic programming approach
L. El Ghaoui, M. Oks, and F. Oustry · 2003
Cited alongside, same era.
Risk reduction in large portfolios: Why imposing the wrong constraints helps
R. Jagannathan and T. Ma · 2003
Cited alongside, same era.
Improved estimation of the covariance matrix of stock returns with an application to portfolio selection
O. Ledoit and M. Wolf · 2003
Cited alongside, same era.
Distributionally robust multi-item newsvendor problems with multimodal demand distributions
G. Hanasusanto, D. Kuhn, S. W. Wallace, and S. Zymler · 2015
Later among the works it cites.
Real-world datasets for portfolio selection and solutions of some stochastic dominance portfolio models
R. Bruni, F. Cesarone, A. Scozzari, and F. Tardella · 2016
Later among the works it cites.
Efficient portfolio selection in a large market
J. Chen and M. Yuan · 2016
Later among the works it cites.
An overview of the estimation of large covariance and precision matrices
J. Fan, Y. Liao, and H. Liu · 2016
Later among the works it cites.
Computationally tractable counterparts of distributionally robust constraints on risk measures
K. Postek, D. den Hertog, and B. Melenberg · 2016
Later among the works it cites.
Limit laws of the empirical Wasserstein distance: Gaussian distributions
T. Rippl, A. Munk, and A. Sturm · 2016
Later among the works it cites.
Robust growth-optimal portfolios
N. Rujeerapaiboon, D. Kuhn, and W. Wiesemann · 2016
Later among the works it cites.
Generalized Gauss inequalities via semidefinite programming
B. P. Van Parys, P. J. Goulart, and D. Kuhn · 2016
Later among the works it cites.
JuMP: A modeling language for mathematical optimization
I. Dunning, J. Huchette, and M. Lubin · 2017
Later among the works it cites.
Tail analysis without parametric models: A worst-case perspective
H. Lam and C. Mottet · 2017
Later among the works it cites.
Robust sample average approximation
D. Bertsimas, V. Gupta, and N. Kallus · 2018
Later among the works it cites.
Strong convexity of sandwiched entropies and related optimization problems
R. Bhatia, T. Jain, and Y. Lim · 2018
Later among the works it cites.
Closed-form solutions for worst-case law invariant risk measures with application to robust portfolio optimization
J. Y.-M. Li · 2018
Later among the works it cites.
Wasserstein Riemannian geometry of Gaussian densities
L. Malagò, L. Montrucchio, and G. Pistone · 2018
Later among the works it cites.
Data-driven distributionally robust optimization using the Wasserstein metric: Performance guarantees and tractable reformulations
P. Mohajerin Esfahani and D. Kuhn · 2018
Later among the works it cites.
Asymmetry and ambiguity in newsvendor models
K. Natarajan, M. Sim, and J. Uichanco · 2018
Later among the works it cites.
Chebyshev inequalities for products of random variables
N. Rujeerapaiboon, D. Kuhn, and W. Wiesemann · 2018
Later among the works it cites.
Wasserstein distributionally robust Kalman filtering
S. Shafieezadeh-Abadeh, V. A. Nguyen, D. Kuhn, and P. Mohajerin Esfahani · 2018
Later among the works it cites.
On the Bures-Wasserstein distance between positive definite matrices
R. Bhatia, T. Jain, and Y. Lim · 2019
Later among the works it cites.
Wasserstein distributionally robust optimization: Theory and applications in machine learning
D. Kuhn, P. Mohajerin Esfahani, V. Nguyen, and S. Shafieezadeh-Abadeh · 2019
Later among the works it cites.
Mean estimation and regression under heavy-tailed distributions: A survey
G. Lugosi and S. Mendelson · 2019
Later among the works it cites.
High-dimensional Statistics: A Non-Asymptotic Viewpoint
M. J. Wainwright · 2019
Later among the works it cites.
Portfolio construction by mitigating error amplification: The bounded-noise portfolio
L. Zhao, D. Chakrabarti, and K. Muthuraman · 2019
Later among the works it cites.
Finite-sample guarantees for Wasserstein distributionally robust optimization: Breaking the curse of dimensionality
R. Gao · 2020
Later among the works it cites.
Optimizing distortion riskmetrics with distributional uncertainty
S. Pesenti, Q. Wang, and R. Wang · 2020
Later among the works it cites.
Learning models with uniform performance via distributionally robust optimization
J. C. Duchi and H. Namkoong · 2021
Closest in time.
Semi-discrete optimal transport: Hardness, regularization and numerical solution
B. Taşkesen, S. Shafieezadeh-Abadeh, and D. Kuhn · 2021
Closest in time.
Distributionally robust mean-variance portfolio selection with Wasserstein distances
J. Blanchet, L. Chen, and X. Y. Zhou · 2022
Closest in time.
Distributionally robust optimization under distorted expectations
J. Cai, J. Li, and T. Mao · 2022
Closest in time.
Distributionally robust inverse covariance estimation: The Wasserstein shrinkage estimator
V. A. Nguyen, D. Kuhn, and P. Mohajerin Esfahani · 2022
Closest in time.
Bridging Bayesian and minimax mean square error estimation via Wasserstein distributionally robust optimization
V. A. Nguyen, S. Shafieezadeh-Abadeh, D. Kuhn, and P. Mohajerin Esfahani · 2023
Closest in time.
A unified theory of robust and distributionally robust optimization via the primal-worst-equals-dual-best principle
J. Zhen, D. Kuhn, and W. Wiesemann · 2023
Closest in time.
RobPy: A Python package for robust statistical methods
S. Leyder, J. Raymaekers, P. J. Rousseeuw, T. Servotte, and T. Verdonck · 2024
Closest in time.
Distributionally robust optimization
D. Kuhn, S. Shafiee, and W. Wiesemann · 2025
Closest in time.