Mathematical Sciences Department Joint Colloquium & Financial Math Seminar
Chao Zhu, University of Wisconsin
Friday, April 4th
11:00am - 12:00 pm
Title: Ergodic Impulse Control with Mean Field Interactions
Abstract: This work analyzes and provides explicit solutions for an ergodic impulse control problem with a specific mean-field interaction. The underlying process is a general one-dimensional diffusion with appropriate boundary behavior. The model is motivated by applications such as the optimal long-term management of renewable natural resources and financial portfolio management. Individual agents aim to maximize their long-term average reward, which consists of a running reward and income from discrete impulses, where the unit intervention price depends on the market through a stationary supply rate. In a competitive market setting, we establish the existence of an equilibrium strategy and provide its explicit characterization within a broad class of policies under mild conditions. Furthermore, we formulate and solve the associated mean-field control problem, where agents cooperate to maximize a common long-term average profit derived from running rewards and impulse actions. To illustrate the theoretical results, we examine a logistic growth model with impulse control.
This is a joint work with Kurt L. Helmes (Humboldt University of Berlin) and Richard H. Stockbridge (University of Wisconsin-Milwaukee).
Bio: Chao Zhu is a professor in the Department of Mathematical Sciences at the University of Wisconsin-Milwaukee. His research interests include stochastic control and stochastic processes and their applications in areas such as mathematical biology, mathematical finance, etc. He received his Ph.D. from Wayne State University under the direction of Prof. George Yin in 2007.