Abstract

In this work, we show that the entropic value at risk (EVaR), which is not a dynamic risk measure in general, can be a finitely-valued dynamic risk measure for at least one scenario. Specifically, for any distribution where the moment generating function (mgf) exists, then there exists a confidence parameter such that EVaR can be a finitely-valued dynamic risk measure. This separates EVaR from other risk measures, such as the value at risk (VaR), which may not be a finitely-valued dynamic risk for any allowable constant confidence parameter value. This result is not unique to EVaR, as we also show that there exists a confidence parameter such that the average value at risk (AVaR)–which does not require the mgf to exist–is also a finite dynamic risk measure. The main focus of this work is EVaR as it has a stronger stochastic ordering guarantee than AVaR. Future work will examine whether EVaR can be a dynamic risk measure for any other cases.

Original languageEnglish (US)
Title of host publicationAIAA Scitech 2019 Forum
PublisherAmerican Institute of Aeronautics and Astronautics Inc, AIAA
ISBN (Print)9781624105784
DOIs
StatePublished - Jan 1 2019
EventAIAA Scitech Forum, 2019 - San Diego, United States
Duration: Jan 7 2019Jan 11 2019

Publication series

NameAIAA Scitech 2019 Forum

Conference

ConferenceAIAA Scitech Forum, 2019
CountryUnited States
CitySan Diego
Period1/7/191/11/19

ASJC Scopus subject areas

  • Aerospace Engineering

Cite this

Axelrod, A., & Chowdhary, G. (2019). A dynamic risk form of entropic value at risk. In AIAA Scitech 2019 Forum (AIAA Scitech 2019 Forum). American Institute of Aeronautics and Astronautics Inc, AIAA. https://doi.org/10.2514/6.2019-0392

A dynamic risk form of entropic value at risk. / Axelrod, Allan; Chowdhary, Girish.

AIAA Scitech 2019 Forum. American Institute of Aeronautics and Astronautics Inc, AIAA, 2019. (AIAA Scitech 2019 Forum).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Axelrod, A & Chowdhary, G 2019, A dynamic risk form of entropic value at risk. in AIAA Scitech 2019 Forum. AIAA Scitech 2019 Forum, American Institute of Aeronautics and Astronautics Inc, AIAA, AIAA Scitech Forum, 2019, San Diego, United States, 1/7/19. https://doi.org/10.2514/6.2019-0392
Axelrod A, Chowdhary G. A dynamic risk form of entropic value at risk. In AIAA Scitech 2019 Forum. American Institute of Aeronautics and Astronautics Inc, AIAA. 2019. (AIAA Scitech 2019 Forum). https://doi.org/10.2514/6.2019-0392
Axelrod, Allan ; Chowdhary, Girish. / A dynamic risk form of entropic value at risk. AIAA Scitech 2019 Forum. American Institute of Aeronautics and Astronautics Inc, AIAA, 2019. (AIAA Scitech 2019 Forum).
@inproceedings{b1dd142d33f649d3bbee2a2321ce1e1d,
title = "A dynamic risk form of entropic value at risk",
abstract = "In this work, we show that the entropic value at risk (EVaR), which is not a dynamic risk measure in general, can be a finitely-valued dynamic risk measure for at least one scenario. Specifically, for any distribution where the moment generating function (mgf) exists, then there exists a confidence parameter such that EVaR can be a finitely-valued dynamic risk measure. This separates EVaR from other risk measures, such as the value at risk (VaR), which may not be a finitely-valued dynamic risk for any allowable constant confidence parameter value. This result is not unique to EVaR, as we also show that there exists a confidence parameter such that the average value at risk (AVaR)–which does not require the mgf to exist–is also a finite dynamic risk measure. The main focus of this work is EVaR as it has a stronger stochastic ordering guarantee than AVaR. Future work will examine whether EVaR can be a dynamic risk measure for any other cases.",
author = "Allan Axelrod and Girish Chowdhary",
year = "2019",
month = "1",
day = "1",
doi = "10.2514/6.2019-0392",
language = "English (US)",
isbn = "9781624105784",
series = "AIAA Scitech 2019 Forum",
publisher = "American Institute of Aeronautics and Astronautics Inc, AIAA",
booktitle = "AIAA Scitech 2019 Forum",

}

TY - GEN

T1 - A dynamic risk form of entropic value at risk

AU - Axelrod, Allan

AU - Chowdhary, Girish

PY - 2019/1/1

Y1 - 2019/1/1

N2 - In this work, we show that the entropic value at risk (EVaR), which is not a dynamic risk measure in general, can be a finitely-valued dynamic risk measure for at least one scenario. Specifically, for any distribution where the moment generating function (mgf) exists, then there exists a confidence parameter such that EVaR can be a finitely-valued dynamic risk measure. This separates EVaR from other risk measures, such as the value at risk (VaR), which may not be a finitely-valued dynamic risk for any allowable constant confidence parameter value. This result is not unique to EVaR, as we also show that there exists a confidence parameter such that the average value at risk (AVaR)–which does not require the mgf to exist–is also a finite dynamic risk measure. The main focus of this work is EVaR as it has a stronger stochastic ordering guarantee than AVaR. Future work will examine whether EVaR can be a dynamic risk measure for any other cases.

AB - In this work, we show that the entropic value at risk (EVaR), which is not a dynamic risk measure in general, can be a finitely-valued dynamic risk measure for at least one scenario. Specifically, for any distribution where the moment generating function (mgf) exists, then there exists a confidence parameter such that EVaR can be a finitely-valued dynamic risk measure. This separates EVaR from other risk measures, such as the value at risk (VaR), which may not be a finitely-valued dynamic risk for any allowable constant confidence parameter value. This result is not unique to EVaR, as we also show that there exists a confidence parameter such that the average value at risk (AVaR)–which does not require the mgf to exist–is also a finite dynamic risk measure. The main focus of this work is EVaR as it has a stronger stochastic ordering guarantee than AVaR. Future work will examine whether EVaR can be a dynamic risk measure for any other cases.

UR - http://www.scopus.com/inward/record.url?scp=85068980257&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85068980257&partnerID=8YFLogxK

U2 - 10.2514/6.2019-0392

DO - 10.2514/6.2019-0392

M3 - Conference contribution

SN - 9781624105784

T3 - AIAA Scitech 2019 Forum

BT - AIAA Scitech 2019 Forum

PB - American Institute of Aeronautics and Astronautics Inc, AIAA

ER -