Entropic Value-at-Risk: A New Coherent Risk Measure

Ahmadi‐Javid, Amir

doi:10.1007/s10957-011-9968-2

Cited by 207 publications

(155 citation statements)

References 33 publications

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“…Examples of risk measures include value-at-risk (VaR), variance (VAR), and Conditional Value at Risk (CVAR). Ahmadi-Javid [2] introduced the Entropic Value at Risk (EVAR) measure that addresses computational and coherency shortcomings of VAR and CVAR.…”

Section: B Entropic Value At Risk (Evar) Risk Measurementioning

confidence: 99%

“…The importance of the EVAR lies in the fact that, with confidence level 1 − γ, it upper bounds the value of the posterior expectation [2]:…”

Section: B Entropic Value At Risk (Evar) Risk Measurementioning

confidence: 99%

“…While such measures describe an expected distance of a sample from the mean of the current stochastic model, neither address how the stochastic model changes as a result of new observations. By contrast, uncertainty measures such as the information gain [1], the entropic value at risk (EVAR) [2], and the conditional value at risk (CVAR) [3] all describe uncertainty in how the model will change due to new observations. While both CVAR and EVAR provide an intuitive bound on how the expectation of our model changes due to new observations, EVAR is more computationally efficient than CVAR and is the tightest upper bound on CVAR [2].…”

Section: Introductionmentioning

confidence: 99%

“…By contrast, uncertainty measures such as the information gain [1], the entropic value at risk (EVAR) [2], and the conditional value at risk (CVAR) [3] all describe uncertainty in how the model will change due to new observations. While both CVAR and EVAR provide an intuitive bound on how the expectation of our model changes due to new observations, EVAR is more computationally efficient than CVAR and is the tightest upper bound on CVAR [2]. As we will show, EVAR can also incorporate the information gain, and so we examine EVAR as a comprehensive measure of the uncertainty in our model.…”

Section: Introductionmentioning

confidence: 99%

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Data-driven prediction of EVAR with confidence in time-varying datasets

Axelrod

Carlone

Chowdhary

et al. 2016

2016 IEEE 55th Conference on Decision and Control (CDC)

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Abstract-The key challenge for learning-based autonomous systems operating in time-varying environments is to predict when the learned model may lose relevance. If the learned model loses relevance, then the autonomous system is at risk of making wrong decisions. The entropic value at risk (EVAR) is a computationally efficient and coherent risk measure that can be utilized to quantify this risk. In this paper, we present a Bayesian model and learning algorithms to predict the state-dependent EVAR of time-varying datasets. We discuss applications of EVAR to an exploration problem in which an autonomous agent has to choose a set of sensing locations in order to maximize the informativeness of the acquired data and learn a model of an underlying phenomenon of interest. We empirically demonstrate the efficacy of the presented model and learning algorithms on four real-world datasets.

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Section: B Entropic Value At Risk (Evar) Risk Measurementioning

confidence: 99%

“…The importance of the EVAR lies in the fact that, with confidence level 1 − γ, it upper bounds the value of the posterior expectation [2]:…”

Section: B Entropic Value At Risk (Evar) Risk Measurementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Data-driven prediction of EVAR with confidence in time-varying datasets

Axelrod

Carlone

Chowdhary

et al. 2016

2016 IEEE 55th Conference on Decision and Control (CDC)

View full text Add to dashboard Cite

show abstract

“…Risk-aversion is an old notion, however with no consensus about its definition (see [24,23,1]). However, any risk measure that is coherent (see [27]) is considered to be a good measure.…”

Section: Introductionmentioning

confidence: 99%

Robust Risk-Averse Stochastic Multi-armed Bandits

Maillard

2013

Lecture Notes in Computer Science

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Abstract. We study a variant of the standard stochastic multi-armed bandit problem when one is not interested in the arm with the best mean, but instead in the arm maximising some coherent risk measure criterion. Further, we are studying the deviations of the regret instead of the less informative expected regret. We provide an algorithm, called RA-UCB to solve this problem, together with a high probability bound on its regret.

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Statistical evaluation of a long‐memory process using the generalized entropic value‐at‐risk

Yoshioka,

Yoshioka

2023

Environmetrics

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The modeling and identification of time series data with a long memory are important in various fields. The streamflow discharge is one such example that can be reasonably described as an aggregated stochastic process of randomized affine processes where the probability measure, we call it reversion measure, for the randomization is not directly observable. Accurate identification of the reversion measure is critical because of its omnipresence in the aggregated stochastic process. However, the modeling accuracy is commonly limited by the available real‐world data. We resolve this issue by proposing the novel upper and lower bounds of a statistic of interest subject to ambiguity of the reversion measure. Here, we use the Tsallis value‐at‐risk (TsVaR) as a convex risk functional to generalize the widely used entropic value‐at‐risk (EVaR) as a sharp statistical indicator. We demonstrate that the EVaR cannot be used for evaluating key statistics, such as mean and variance, of the streamflow discharge due to the blowup of some exponential integrand. We theoretically show that the TsVaR can avoid this issue because it requires only the existence of some polynomial moment, not exponential moment. As a demonstration, we apply the semi‐implicit gradient descent method to calculate the TsVaR and corresponding Radon–Nikodym derivative for time series data of actual streamflow discharges in mountainous river environments.

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Entropic Value-at-Risk: A New Coherent Risk Measure

Cited by 207 publications

References 33 publications

Data-driven prediction of EVAR with confidence in time-varying datasets

Data-driven prediction of EVAR with confidence in time-varying datasets

Robust Risk-Averse Stochastic Multi-armed Bandits

Statistical evaluation of a long‐memory process using the generalized entropic value‐at‐risk

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