{"title":"Nonasymptotic Estimation of Risk Measures Using Stochastic Gradient Langevin Dynamics","authors":"Jiarui Chu, Ludovic Tangpi","doi":"10.1137/23m1552747","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Financial Mathematics, Volume 15, Issue 2, Page 503-536, June 2024. <br/> Abstract.In this paper we will study the approximation of some law-invariant risk measures. As a starting point, we approximate the average value at risk using stochastic gradient Langevin dynamics, which can be seen as a variant of the stochastic gradient descent algorithm. Further, the Kusuoka spectral representation allows us to bootstrap the estimation of the average value at risk to extend the algorithm to general law-invariant risk measures. We will present both theoretical, nonasymptotic convergence rates of the approximation algorithm and numerical simulations.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"96","ListUrlMain":"https://doi.org/10.1137/23m1552747","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
SIAM Journal on Financial Mathematics, Volume 15, Issue 2, Page 503-536, June 2024. Abstract.In this paper we will study the approximation of some law-invariant risk measures. As a starting point, we approximate the average value at risk using stochastic gradient Langevin dynamics, which can be seen as a variant of the stochastic gradient descent algorithm. Further, the Kusuoka spectral representation allows us to bootstrap the estimation of the average value at risk to extend the algorithm to general law-invariant risk measures. We will present both theoretical, nonasymptotic convergence rates of the approximation algorithm and numerical simulations.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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