In this talk, we are concerned with the expected values of certain functionals of the path of a stochastic process during a given time period. High-order asymptotic characterizations of such values when the time period shrinks to 0 have a wide range of applications. In statistics, they are crucial in obtaining the infill asymptotic properties of high-frequency based statistical methods of stochastic processes. In finance, they have been used as model selection and calibration tools based on near expiration option prices. In some Engineering problems, they also show up as a method to solve a problem in continuous time by looking at the analogous problem in discrete time and shrinking the time step. These short-time asymptotic methods are especially useful to study complex models with jumps and stochastic volatility due to the lack of tractable formulas and efficient numerical procedures. In this talk, I will discuss some recent advances in the area and illustrate their broad relevance in several contexts.

Short Bio:

José Figueroa-López is a full Professor of Mathematics at Washington University in St. Louis. Formerly he was Associate Professor of Statistics at Purdue University, where he served as associate director of the Computational Finance Program. Professor Figueroa’s ongoing research includes short-time asymptotics of jump-diffusion models, diffusion limits of Limit Order Book models, optimal limit order placement problems, and optimal tuning of high-frequency based econometric methods. He was awarded the NSF career award in 2012 and currently has two active NSF grants on the interplay of finance, statistics, and probability. He is Associate Editor of the SIAM Journal on Financial Mathematics (SIFIN) and a former Associate Editor of Electronic Journal of Statistics.

Tea before in SAS 4104, 3:30-4:00.