AN OLD‐NEW CONCEPT OF CONVEX RISK MEASURES: THE OPTIMIZED CERTAINTY EQUIVALENT

By Aharon Ben-Tal, Marc Teboulle. 2007

470 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/6c0d0f80cec4ef8895ffc68a8e390a69ad8f7d81

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Citations in the corpus

Distributionally Robust Optimization and Its Tractable Approximations (2010, methodology): “Furthermore, the -CVaR can be derived as a special case of the negative optimized certainty equivalent (OCE) introduced by Ben-Tal and Teboulle (1986, 2007).”
Entropic Value-at-Risk: A New Coherent Risk Measure (2012, background): “2 of [47].”
Haezendonck-Goovaerts risk measures and Orlicz quantiles (2012, background): “The first order condition (7) becomes ∥∥(X − x∗) ∥∥ 1 = (1− α) 1 2 ∥∥(X − x∗) ∥∥ 2 (14)”
Stochastic model-based minimization of weakly convex functions (2018, background): “Nonlinear least squares, phase retrieval [23,30,34], minimization of the Conditional Value-at-Risk [7, 8,60], graph synchronization [2,6,63], covariance estimation [17], and robust principal component analysis [11,14] naturally lead to weakly convex formulations.”
Distributionally Robust Optimization: A Review (2019, methodology): “They illustrate that the ambiguity sets formed via φ-divergences are related to an optimized certainty equivalent risk measure formed via φ-functions [23].”
Deep hedging (2018, background): “Taking (x) := −u(−x) (x ∈ R) for a utility function u : R → R, (6) coincides with the optimized certainty equivalent as defined (and studied in a lot more detail than here) in Ben-Tal and Teboulle (2007).”
Coherent Approaches to Risk in Optimization Under Uncertainty (2007, background): “Ben-Tal and Teboulle [5] open this further and note that E[a(Q)] has been studied for more general a than a(Q) = [Q logQ], as in (6.”
Robust empirical optimization is almost the same as mean-variance optimization (2018, unknown): “This is a regular measure of risk [18] (or optimized certainty equivalent [4]) which is a generalization of CVaR.”
Distributionally Robust Convex Optimization (2014, background): “In a similar way, we can generalize the distributionally robust constraint (3) to safeguarding constraints based on the shortfall risk measure [30] and the optimized certainty equivalent [9].”
Fairness risk measures (2019, background): “Our relating of fairness and risk measures motivates study of risk measures beyond CVaR, e.g., spectral measures [Acerbi, 2002], optimised certainty equivalents [Ben-Tal and Teboulle, 2007], & entropic value at risk [Ahmadi-Javid, 2012].”
Generalized Quantiles as Risk Measures (2014, methodology): “Similar characterizations have been obtained by Ben-Tal and Teboulle (2007) and Weber (2006) under slightly different hypotheses, so we provide an independent proof.”
Adapted Wasserstein distances and stability in mathematical finance (2019, background): “iant risk measure which satises ˆ() ˆ() Ldw(;) for some constant Ldepending on the p-the moment of and is the optimized certainty equivalent, introduced to the mathematical nance community in [17]. For a convex, increasing function ‘: R !R which is bounded from below and satises ‘(x)=x!1as x!1, the ”
TRACTABLE ROBUST EXPECTED UTILITY AND RISK MODELS FOR PORTFOLIO OPTIMIZATION (2010, unknown): “It is shown in (Ben-Tal and Teboulle 2007), that for this class of utility functions, ρu(x̃) satisfies the properties in Definition 3.1 and defines a convex risk measure.”
Statistical estimation of composite risk functionals and risk optimization problems (2015, background): “Many of the risk measures of interest can be expressed via optimization of the so-called optimized certainty equivalent (Ben-Tal and Teboulle 2007) for a suitable choice of the utility function.”