In this talk, I will present a tractable sufficient condition for the consistency of maximum likelihood estimators (MLEs) in partially observed diffusion models, stated explicitly via the stationary distribution of the fully observed system. This result is then applied to a model of market microstructure with latent (unobserved) price process, for which the estimation is performed using real market data for liquid NASDAQ stocks. In particular, we obtain an estimate of the price impact coefficient, as well as the micro-level volatility and the drift of the latent price process (the latter is responsible for the concavity of expected price impact of a large meta-order). Joint work with Y. Yin.

Bio: Sergey Nadtochiy is a Professor of Applied Mathematics at Illinois Tech. Prior to this he was an Assistant Professor in Mathematics at University of Michigan and a Research Fellow in Oxford-Man Institute at Oxford University. Sergey received his PhD from Princeton University in the Department of Operations Research and Financial Engineering in 2009. In his research, Sergey solves problems in Probability and PDEs motivated by applications in Finance/Economics, Physics and Statistics.