COMONOTONIC MEASURES OF MULTIVARIATE RISKS

By Ivar Ekeland, Alfred Galichon, Marc Henry. 2012

118 citations recorded by the source corpus.

We propose a multivariate extension of a well‐known characterization by S. Kusuoka of regular and coherent risk measures as maximal correlation functionals. This involves an extension of the notion of comonotonicity to random vectors through generalized quantile functions. Moreover, we propose to replace the current law invariance, subadditivity, and comonotonicity axioms by an equivalent property we call strong coherence and that we argue has more natural economic interpretation. Finally, we reformulate the computation of regular and coherent risk measures as an optimal transportation problem, for which we provide an algorithm and implementation.

Subfields: Economics and Econometrics, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/70ae9680ff2c0dff60a696b852f5f8360535589b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

1. Ilya S. Molchanov
2. Victor Chernozhukov
3. Alfred Galichon
4. Marc Hallin
5. Ignacio Cascos
6. Guillaume Carlier
7. Marc Henry
8. A. Rosen

In Finance

1. Victor Chernozhukov
2. Guillaume Carlier
3. Alfred Galichon
4. Marc Hallin
5. Ilya S. Molchanov
6. Ignacio Cascos
7. Marc Henry
8. Roger W. Koenker

In Management Science and Operations Research

1. Alfred Galichon
2. Ilya S. Molchanov
3. Victor Chernozhukov
4. Marc Henry
5. Ignacio Cascos
6. Marc Hallin
7. Guillaume Carlier
8. Juan Antonio Cuesta-Albertos

Citations in the corpus

• Vector Quantile Regression (2014, background): “This form also connects to unconditional multivariate quantile maps defined in [13], who employed them for purposes of risk analysis; our definition given in the previous section is more satisfactory, because it does not require any moment conditions, as follows from the results of [24].”
• Distribution and quantile functions, ranks and signs in dimension d: A measure transportation approach (2021, methodology): “They are the basis, however, of Carlier et al. (2016)’s method of vector quantile regression and Chernozhukov et al. (2017)’s concept of Monge-Kantorovich depth and related quantiles, ranks and signs, two papers of which Ekeland et al. (2012) can be considered a precursor.”
• Vector quantile regression beyond correct specification (2016, methodology): “The notion of vector quantile was recently introduced by Ekeland, Galichon and Henry [5], Galichon and Henry [8] and was used in the framework of quantile regression in our companion paper [4].”
• MULTIVARIATE RISK MEASURES: A CONSTRUCTIVE APPROACH BASED ON SELECTIONS (2013, methodology): “The constructed real-valued risk measure depends on set-valued portfolio X and so cannot be directly related to the framework of [2, 7, 25], since the risk measures considered there depend on random vectors without using the corresponding exchange cones.”
• Monge-Kantorovich Depth, Quantiles, Ranks and Signs (2014, methodology): “Previous proposals have been made, however, of measure transportation-based vector quantile functions in Ekeland, Galichon and Henry [18] and Galichon and Henry [19] (with moment conditions) and Carlier, Chernozhukov and Galichon [5] (dropping moment conditions) who also extended the notion to vecto”