Peter Carr Seminar Series: Ronnie Sircar and Ruimeng Hu

4 pm | Ronnie Sircar

Title

Mean Field Games of Stochastic Intensity Control

Abstract

We discuss some mean field games of stochastic intensity control with applications to ticket pricing, income inequality and cryptocurrency mining. For the first problem, one way to capture both the elastic and stochastic reaction of purchases to price is through a model where sellers control the intensity of a counting process, representing the number of sales thus far. The intensity describes the probabilistic likelihood of a sale, and is a decreasing function of the price a seller sets. A classical model for ticket pricing, which assumes a single seller and infinite time horizon, is by Gallego and van Ryzin (1994) and it has been widely utilized by airlines, for instance. Extending to more realistic settings where there are multiple sellers, with finite inventories, in competition over a finite time horizon is more complicated both mathematically and computationally. We discuss a dynamic mean field game of this type, and some numerical and existence results.

Bio

Ronnie Sircar is the Eugene Higgins Professor of Operations Research and Financial Engineering (ORFE) at Princeton University, and is affiliated with the Bendheim Center for Finance, the Program in Applied and Computational Mathematics, and the Andlinger Center for Energy and the Environment. He received his doctorate from Stanford University, and taught for three years at the University of Michigan in the Department of Mathematics. He has received continuing National Science Foundation research grants since 1998. He was a recipient of the E-Council Excellence in Teaching Award for his teaching in 2002, 2005 and 2006, and the Howard B. Wentz Jr. Junior Faculty Award in 2003. His research interests center on Financial Mathematics, stochastic volatility models, energy markets and exhaustible resources, credit risk, asymptotic and computational methods, portfolio optimization and stochastic control problems, and stochastic differential games. He is a co-author of the book “Multiscale Stochastic Volatility for Equity, Interest-Rate and Credit Derivatives”, published by Cambridge University Press in 2011, and was founding co-editor-in-chief of the SIAM Journal on Financial Mathematics, from 2009-2015. He was Director of Graduate Studies for the Master in Finance program at the Bendheim Center for Finance from 2015-2018. He was Chair of the ORFE department from 2018-2024. He was made a Fellow of the Society for Industrial and Applied Mathematics (SIAM) in 2020 for “contributions to financial mathematics and asymptotic methods for stochastic control and differential games.”

5 pm | Ruimeng Hu

Title

A Stochastic Control Model for Strategic Misdirection via Sequential Hypothesis Testing

Abstract

Concealing intentions and sending misleading signals to confuse opponents is an interesting yet challenging problem in multi-player games due to its inherently ill-posed nature. In this talk, we introduce a well-interpretable linear-quadratic stochastic control framework that models such strategic interactions between two opposing teams, red and blue. A key novelty of our approach is the incorporation of sequential hypothesis testing to model the inference of intentions. Our work consists of two main parts: firstly, we derive optimal misdirection strategies for the blue team, who aim to achieve a primary objective while minimizing the extent to which its intentions are revealed to the red team. In addition, we extend the model to a Stackelberg game, where the red team, aware of the blue team's optimal behavior, strategically leaks information to deceive the blue team into inadvertently exposing its true intentions. We demonstrate through numerical experiments that our model effectively captures the essence of strategic misdirection.

Bio

Ruimeng Hu is an Associate Professor at the University of California, Santa Barbara, with a joint appointment in the Department of Mathematics, and the Department of Statistics and Applied Probability. From 2018 to 2020, she was a term assistant professor at Columbia University. Her current research interests include stochastic differential games and mean-field games, machine learning and its intersections with stochastic analysis, and stochastic PDE. Her research is supported by NSF and ONR.