Mathematical Finance and Stochastics Seminar by Lane Chun Yeung: Large-Scale Limits of Interacting Particle Systems
Speaker: Lane Chun Yeung, assistant professor of applied mathematics, Illinois Institute of Technology
Title: Large-Scale Limits of Interacting Particle Systems
Abstract: Interacting particle systems are used to model a wide variety of phenomena in statistical physics, neuroscience, financial portfolio theory, and biology. This talk begins with an overview of the large-scale behavior of systems with mean-field (symmetric) interactions. Under this symmetry, one can pass to a continuum (infinite-particle) limit that effectively describes the macroscopic behavior. Two recent extensions will be discussed: (i) a mean-field limit for rank-based models with common noise arising in stochastic portfolio theory; and (ii) heterogeneous, non-exchangeable systems, in which approximate independence can be quantified, and decentralized strategies for high-dimensional stochastic control are shown to be near-optimal. A brief outlook on future directions will be discussed along the way.
Stochastic Analysis