Tsallis value-at-risk: generalized entropic value-at-risk

Zou, Zhenfeng; Xia, Zichao; Hu, Taizhong

doi:10.1017/s0269964822000444

Cited by 2 publications

(11 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A duality result between the TsVaRs and corresponding nonlinear expectations are provided, which serves as a pathway to obtain the worst-case distorted reversion measures. For the upper-TsVaR with 0 < q < 1 − 𝛼 −1 , the following relationship holds true by the direct application of Lemmas 3.6 and 3.7, and Theorem 3.8 of Zou et al (2022) to our setting:…”

Section: Dualitymentioning

confidence: 87%

“…TsVaR has been considered for the worst-case overestimation of a random variable of interest because the main motivation for its development was the evaluation of tail risks (Zou et al, 2022). However, we are considering not only the upper bound of a statistic but also the lower bound.…”

Section: Objective and Contributionmentioning

confidence: 99%

“…We consider the ambiguity in the sense of Tsallis (e.g., Zou et al (2022)), which means that the inverse moment R should be effectively replaced by the following distorted one…”

Section: Model Ambiguitymentioning

confidence: 99%

“…in Section 4. The upper-Tsallis value-at-risk (upper-TsVaR) in this paper is the TsVaR of Zou et al (2022) to give an upper bound of the expectation of a random variable by using a convex risk functional.…”

Section: Upper Tsallis Value-at-riskmentioning

confidence: 99%

“…The function g(𝜆) is motivated from the Chernoff inequality (Zou et al, 2022) of a sharp upper bound of the probability Pr…”

Section: Upper Tsallis Value-at-riskmentioning

confidence: 99%

See 4 more Smart Citations

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

Yoshioka,

Yoshioka

2023

Environmetrics

View full text Add to dashboard Cite

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.

show abstract

Section: Dualitymentioning

confidence: 87%

Section: Objective and Contributionmentioning

confidence: 99%

“…We consider the ambiguity in the sense of Tsallis (e.g., Zou et al (2022)), which means that the inverse moment R should be effectively replaced by the following distorted one…”

Section: Model Ambiguitymentioning

confidence: 99%

Section: Upper Tsallis Value-at-riskmentioning

confidence: 99%

“…The function g(𝜆) is motivated from the Chernoff inequality (Zou et al, 2022) of a sharp upper bound of the probability Pr…”

Section: Upper Tsallis Value-at-riskmentioning

confidence: 99%

See 3 more Smart Citations

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

Yoshioka,

Yoshioka

2023

Environmetrics

View full text Add to dashboard Cite

show abstract

Orlicz risks for assessing stochastic streamflow environments: a static optimization approach

Yoshioka,

Tomobe,

Yoshioka

2023

Stoch Environ Res Risk Assess

View full text Add to dashboard Cite

This study applies novel risk measures, called Orlicz risks, to the risk and uncertainty evaluation of the streamflow discharge as a primary driver of hydrological and hydraulic processes of interest in civil and environmental engineering. We consider the mixed moving average process governing the discharge whose statistics are explicitly represented as some product of a time-scale characterizing the flow attenuation and a jump moment governing the size and frequency of jumps. The classical Orlicz risks are extended so that not only the upper tail risk but also the lower one of the jump size and attenuation of the discharge can be evaluated within a single mathematical framework. Further, the risk and uncertainty can be individually quantified in a tractable manner by the proposed Orlicz risks. Computing the Orlicz risks reduces to solving a pair of novel static optimization problems that are solvable semi-analytically. The risk and uncertainty involved in the streamflow dynamics can be consistently evaluated by specifying few user-dependent parameters. The associated Radon–Nikodym derivatives as the worst-case model uncertainties are obtained as byproducts. Sufficient conditions for the well-posedness of the Orlicz risks are discussed and numerical algorithms for computing them are presented. We finally apply the proposed framework to a statistical analysis of the streamflow discharge time series data collected at mountainous river environments.

show abstract

Tsallis value-at-risk: generalized entropic value-at-risk

Cited by 2 publications

References 19 publications

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

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

Orlicz risks for assessing stochastic streamflow environments: a static optimization approach

Contact Info

Product

Resources

About