Non-asymptotic estimation of risk measures using stochastic gradient Langevin dynamics

Abstract

In this paper we will study the approximation of arbitrary 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's 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, non-asymptotic convergence rates of the approximation algorithm and numerical simulations.

References in corpus (5)

• Transportation cost-information inequalities and applications to random dynamical systems and diffusions
• Statistical Learning with Conditional Value at Risk
• A Contour Stochastic Gradient Langevin Dynamics Algorithm for Simulations of Multi-modal Distributions
• Adaptively Preconditioned Stochastic Gradient Langevin Dynamics
• A fully data-driven approach to minimizing CVaR for portfolio of assets via SGLD with discontinuous updating