Stochastic & Multiscale Modeling and Computation Seminar by Pei Liu: Nonparametric Bayesian volatility estimation for gamma-driven stochastic differential equations

Speaker:

Pei Liu, College of Science and Engineering, University of Minnesota

Title:
Nonparametric Bayesian volatility estimation for gamma-driven stochastic differential equations

Abstract: We study a nonparametric Bayesian approach to estimating the volatility function of a stochastic differential equation (SDE) driven by a gamma process. The volatility function is assumed to be positive and piecewise constant or Hölder continuous. We first show that the SDE admits a weak solution under a simple growth condition, which is unique in law. In the statistical problem, the volatility function is always modeled a priori as a piecewise constant on a partition of the real line, and we specify a gamma prior to its coefficients. This leads to a straightforward procedure for posterior inference. We show that the contraction rate of the posterior distribution is root n (sample size) for piecewise constant volatility and depends on the Hölder exponent in the other case. Joint work with Denis Belomestny, Shota Gugushvili, and Moritz Schauer. 

Meeting ID: 894 8470 9359

Passcode: 365404

Stochastic & Multiscale Modeling and Computation