Remarks on quantiles and distortion risk measures

By Jan Dhaene, Alexander Kukush, Daniël Linders, Qihe Tang. 2012

124 citations recorded by the source corpus.

Subfields: Finance, Management Science and Operations Research, Ocean Engineering

How researchers see this paper

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

In Finance

1. Carole Bernard
2. David Silver
3. R´emi Munos
4. Georg Ostrovski
5. Will Dabney
6. Steven Vanduffel
7. Silvana M. Pesenti

In Management Science and Operations Research

1. David Silver
2. R´emi Munos
3. Will Dabney
4. Georg Ostrovski
5. Carole Bernard
6. Marc G. Bellemare
7. Steven Vanduffel
8. Silvana M. Pesenti

In Ocean Engineering

1. David Silver
2. R´emi Munos
3. Georg Ostrovski
4. Will Dabney
5. Steven Vanduffel
6. Carole Bernard
7. Silvana M. Pesenti

Citations in the corpus

• Implicit Quantile Networks for Distributional Reinforcement Learning (2018, background): “…value of The immediate implication of this is that for any β , there exists a sampling distribution for τ such that the mean of Z τ is equal to the distorted expectation of Z under β , that is, any distorted expectation can be represented as a weighted sum over the quantiles (Dhaene et al., 2012).”
• QUOTA: The Quantile Option Architecture for Reinforcement Learning (2018, unknown): “The expectation of the utility-function-distorted valued distribution can be interpreted as a weighted sum of quantiles (Dhaene et al. 2012), meaning that quantile-based action selection implicitly adopts the idea of utility function.”
• Robust distortion risk measures (2022, background): “Both VaR and VaR are distortion risk measures (VaRα with g(x) = 1(1−α,1](x) and VaR + α with g(x) = 1[1−α,1](x), see Dhaene et al. (2012)); however, they do not belong to the class of distortion risk measures considered in this paper as they do not satisfy Assumption 1.”