Mathematical Finance, Stochastic Analysis, and Machine Learning Seminar by Sergey Nadtochiy:

Our next talk in the seminar on Fin. Math., Stochastic Analysis and Machine Learning will be given on Tue, Oct 8, at 12:50-1:50pm, in RE 119. This is an in-person talk.

Speaker: Sergey Nadtochiy, professor of applied mathematics, Illinois Institute of Technology

Title: Consistency of MLE in Partially Observed Diffusion Models on a Torus.

Abstract: Partially observed (a.k.a. hidden) Markov models appear in a wide variety of applications. When the (static) parameters of such a model are known, the unobserved coordinates of the diffusion process (a.k.a. signal) can be approximated based on the observed coordinates via stochastic filtering. But what shall one do if the parameters of the model also need to be estimated? In the classical parametric statistics, the maximum likelihood estimator (MLE) is expected to have the best asymptotic properties, as the size of the observed sample increases. These properties are easy to prove in a basic setting with i.i.d. observations, but establishing them in a more complex model, such as a partially observed Markov model, presents significant challenges. In my talk, I will focus on proving the consistency of MLE — i.e. its convergence to a true parameter value — in partially observed diffusion models with periodic coefficients. This result is new, although analogous results are available for discrete-space and discrete-time partially observed Markov models. I will describe the financial problem that served as a motivation for this study and will explain the novel approach we developed for proving the consistency of MLE, which allows us to obtain sharper results with less convoluted proofs and under verifiable assumptions. Joint work with I. Ekren.

Mathematical Finance, Stochastic Analysis, and Machine Learning Seminar