Identifier,"Start Date / Time","End Date / Time",Title,Subtitle,Type,Description,Permalink,"Building Name",Room,"Location Name",Cost,Tags,Sponsors
114233-21832531,"2024-03-13 16:00:00","2024-03-13 17:00:00","Generalization of Shapley's cooperative value allocation theory via random coalition process","Tongseok Lim, Purdue","Workshop / Seminar","Lloyd Shapley’s cooperative value allocation theory is a central concept in game theory that is widely applied in various fields to assess individual contributions and allocate resources. The Shapley value formula and his four defining axioms form the foundation of the theory.
We interpret the Shapley value as an expectation of a certain stochastic path integral, with each path representing a general coalition process. As a result, the value allocation is naturally extended to all partial coalition states. Furthermore, the new allocation scheme can be readily generalized by path-integrating various edge flows, which we refer to as the f-Shapley value. Finally, by employing Hodge theory on graphs, we show how to compute the stochastic path integral via the graph Poisson equation.",https://events.umich.edu/event/114233,"East Hall",1360,"East Hall",,Mathematics,"Financial/Actuarial Mathematics Seminar - Department of Mathematics"
110936-21825883,"2024-03-20 16:00:00","2024-03-20 17:00:00","Democratizing or Demoralizing: The Impact of Robinhood on Trading Costs and Volatility","Mehmet Saglam, University of Cincinatti","Workshop / Seminar","Order collaring, the automatic conversion of default market orders into limit orders with 5% spread over prior prices, has been utilized at Robinhood to protect retail investors from trading at unfavorable prices. In this paper, we provide empirical evidence that this policy harms retail traders in the form of higher trading costs. Using two quasi-experiments involving Robinhood’s trading hours and the discontinuity around 5% spread, we find that Robinhood customers have higher likelihood of paying extreme spreads over close prices. Further, the policy is associated with extreme price movements in stocks. We estimate that the economic loss of the retail traders due to order collaring is on the order of millions of dollars per day.",https://events.umich.edu/event/110936,"East Hall",1360,"East Hall",,Mathematics,"Financial/Actuarial Mathematics Seminar - Department of Mathematics"
118407-21841044,"2024-03-27 16:00:00","2024-03-27 17:00:00","Non-parametric estimations for graphon mean-field particle systems","Hongyi Zhou (UM)","Workshop / Seminar","We consider the graphon mean-field system introduced by Bayraktar et al. in Bayraktar, Chakraborty, Wu (AAP 2023)
which is the large-population limit of a heterogeneously interacting diffusive particle system.
The interaction is of mean-field type with weights characterized by an underlying graphon function.
Via continuous observations of the trajectories of the finite-population particle system,
we build plug-in estimators of the particle densities, drift coefficients, and graphon interaction weights of the mean-field system.
Our estimators for the densities and drifts are direct results of kernel interpolation on the empirical data, and a deconvolution method leads to an estimator of the underlying graphon function
We prove that the estimator converges to the true graphon function as the number of particles tends to infinity when all other parameters are properly chosen.
Besides, we also conduct a minimax analysis on the plug-in estimator of the particle densities within a particular class of particle systems, which justifies its pointwise optimality.
Joint work with Erhan Bayraktar",https://events.umich.edu/event/118407,"East Hall",1360,"East Hall",,Mathematics,"Financial/Actuarial Mathematics Seminar - Department of Mathematics"
111486-21827175,"2024-04-03 16:00:00","2024-04-03 17:00:00","Mean-Field Games for Scalable Computation and Diverse Applications","Wuchen Li/ University of South Carolina","Workshop / Seminar","Mean field games (MFGs) study strategic decision-making in large populations where individual players interact via specific mean-field quantities. They have recently gained enormous popularity as powerful research tools with vast applications. For example, the Nash equilibrium of MFGs forms a pair of PDEs, which connects and extends variational optimal transport problems. This talk will present recent progress in this direction, focusing on computational MFG and engineering applications in robotics path planning, pandemics control, and Bayesian/AI sampling algorithms. This is based on joint work with the MURI team led by Stanley Osher (UCLA).",https://events.umich.edu/event/111486,"East Hall",1360,"East Hall",,Mathematics,"Financial/Actuarial Mathematics Seminar - Department of Mathematics"
114835-21833674,"2024-04-10 16:00:00","2024-04-10 17:00:00","Optimal win martingale","XIn Zhang/ University of Alabama","Workshop / Seminar","A prediction market is a market where people can trade based on the outcomes of future events. It is widely used in sports games, elections, and the pricing of digital options. In math finance, prediction markets can be modeled by the so-called win martingales, continuous time martingales that end up with Bernoulli distributions. In this talk, choosing specific divergences as objective functionals, we will solve a class of optimal win martingale. In some cases, we will get explicit formulas of optimizers, and make connections between Schrödinger and filtering problems. Based on the joint work with Julio Backhoff.",https://events.umich.edu/event/114835,"East Hall",1360,"East Hall",,Mathematics,"Financial/Actuarial Mathematics Seminar - Department of Mathematics"
112183-21828569,"2024-04-17 16:00:00","2024-04-17 17:00:00","Utilizing game theory and deep learning to find optimal policies for large number of agents","Gokce Dayanikli, UIUC","Workshop / Seminar","In many real-life policy making applications, the principal (i.e., governor or regulator) would like to find optimal policies for a large population of interacting agents who optimize their own objectives in a game theoretical framework. With the motivation of finding optimal policies for large populations, we start with introducing continuous time Stackelberg mean field game problem between a principal and a large number of agents. In the model, the agents in the population play a non-cooperative game and choose their controls to optimize their individual objectives while interacting with the principal and the other agents in the society through the population distribution. The principal can influence the resulting mean field game Nash equilibrium through incentives to optimize her own objective. Therefore, Stackelberg mean field game problems are by their nature bi-level problems where we have an optimal control problem at the principal level and a Nash equilibrium problem at the population level. This bi-level nature creates many efficiency challenges for the implementation of numerical approaches. For this reason, we will analyze how to rewrite this bi-level problem as a single-level problem and propose a deep learning approach to solve it. Then we will briefly discuss the convergence of the numerical solution where we utilize the single level problem to the solution of the original problem. We will conclude by demonstrating some applications such as the systemic risk model for a regulator and many banks and an optimal contract problem between a project manager and a large number of employees.",https://events.umich.edu/event/112183,"East Hall",1360,"East Hall",,Mathematics,"Financial/Actuarial Mathematics Seminar - Department of Mathematics"