# Daniel Lacker

#### ASSISTANT PROFESSOR OF INDUSTRIAL ENGINEERING AND OPERATIONS RESEARCH

306 S.W. Mudd

#### Research Interests

Mean field games, interacting particle systems, stochastic optimal control, stochastic games, large deviations, concentration of measureDaniel Lacker works at the intersection of applied probability, stochastic analysis, and mathematical finance. His primary research areas—mean field game theory and interacting particle systems—form the mathematical foundation for a wide range of models of large-scale systems of interacting agents. This modeling framework originated in statistical physics and, more recently, has been adapted to serve a variety of applications in the social sciences, such as financial markets, income inequality, and pedestrian crowd dynamics.

It is common in physics to approximate a large collection of discrete particles, such as those constituting a fluid, by modeling a continuum of particles. Continuous models are often much easier to analyze or simulate, and this approximation procedure has been made mathematically rigorous. On the other hand, recent extensions of these models for social scientific applications are not yet well understood. A main objective of Daniel's research is to mathematically justify and quantify these ubiquitous "mean field" approximations as they arise in new and increasingly complex areas of application, particularly game theory.

Daniel was an NSF postdoctoral fellow in the Division of Applied Mathematics at Brown University from 2015-2017. He received his PhD from Princeton University in 2015 and his BS from Carnegie Mellon University in 2010, and in 2015 he was an Invited Fellow at the Institute for Pure and Applied Mathematics Program on Broad Perspectives and New Directions in Financial Mathematics.

## Research Experience

National Science Foundation Postdoctoral Fellow, Brown University, 2015-2017

## Professional Affiliations

Society for Industrial and Applied Mathematics, Activity Group on Financial Mathematics and Engineering (SIAG/FME)

## Honors & Awards

Winner of the SIAG/FME Conference Paper Prize, 2014

## Selected Publications

- D. Lacker and K. Ramanan, “Rare Nash equilibria and the price of anarchy in large static games,” to appear in
*Mathematics of Operations Research*(2018). - D. Lacker, “Limit theory for controlled McKean-Vlasov dynamics,”
*SIAM Journal on Control and Optimization*55 (3), 1641-1672 (2017). - D. Lacker, “A general characterization of the mean field limit for stochastic differential games,”
*Probability Theory and Related Fields*165 (3), 581-648 (2016). Winner of the SIAG/FME Conference Paper Prize, 2014. - R. Carmona, F. Delarue, and D. Lacker, “Mean field games with common noise,”
*The Annals of Probability*44 (6), 3740-3803 (2016). - D. Lacker, “Mean field games via controlled martingale problems: Existence of Markovian equilibria,”
*Stochastic Processes and their Applications*125 (7), 2856-2894 (2015). - R. Carmona and D. Lacker, “A probabilistic weak formulation of mean field games and applications,”
*The Annals of Applied Probability*25 (3), 1189-1231 (2015). - D. Lacker, “Liquidity, risk measures, and concentration of measure,” to appear in
*Mathematics of Operations Research*(2018).