Nonasymptotic Estimation of Risk Measures Using Stochastic Gradient Langevin Dynamics

IF 1.4 4区经济学 Q3 BUSINESS, FINANCE

SIAM Journal on Financial Mathematics Pub Date : 2024-06-07 DOI:10.1137/23m1552747

Jiarui Chu, Ludovic Tangpi

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.

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利用随机梯度朗文动力学对风险度量进行非渐近估计

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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来源期刊

SIAM Journal on Financial Mathematics MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

2.30

自引率

10.00%

发文量

期刊介绍： SIAM Journal on Financial Mathematics (SIFIN) addresses theoretical developments in financial mathematics as well as breakthroughs in the computational challenges they encompass. The journal provides a common platform for scholars interested in the mathematical theory of finance as well as practitioners interested in rigorous treatments of the scientific computational issues related to implementation. On the theoretical side, the journal publishes articles with demonstrable mathematical developments motivated by models of modern finance. On the computational side, it publishes articles introducing new methods and algorithms representing significant (as opposed to incremental) improvements on the existing state of affairs of modern numerical implementations of applied financial mathematics.