利用随机梯度朗文动力学对风险度量进行非渐近估计

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-06-07 DOI:10.1137/23m1552747

Jiarui Chu, Ludovic Tangpi

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引用次数: 0

摘要

SIAM 金融数学期刊》，第 15 卷，第 2 期，第 503-536 页，2024 年 6 月。摘要.本文将研究一些定律不变风险度量的近似。首先，我们使用随机梯度朗格文动力学来逼近平均风险值，这可以看作是随机梯度下降算法的一种变体。此外，通过 Kusuoka 频谱表示，我们可以对平均风险值的估计进行引导，从而将算法扩展到一般的不变式风险度量。我们将介绍近似算法的理论非渐近收敛率和数值模拟。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Nonasymptotic Estimation of Risk Measures Using Stochastic Gradient Langevin Dynamics

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.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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.