Nonasymptotic Estimation of Risk Measures Using Stochastic Gradient Langevin Dynamics

Jiarui Chu, Ludovic Tangpi

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)503-536
Number of pages34
JournalSIAM Journal on Financial Mathematics
Issue number2
StatePublished - 2024

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Finance
  • Applied Mathematics


  • average value at risk
  • convex risk measure
  • risk minimization
  • stochastic gradient Langevin
  • stochastic optimization


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