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BEGIN:VEVENT
DTSTAMP:20231220T224222
DTSTART;TZID=America/Detroit:20240221T170000
DTEND;TZID=America/Detroit:20240221T180000
SUMMARY:Workshop / Seminar:On Perturbations of Preferences and Indifference Price Invariance
DESCRIPTION:We investigate indifference pricing under perturbations of preferences in small and large markets. We establish stability results for small perturbations of preferences\, where the latter can be stochastic. We obtain a sharp condition in terms of the associated concave and convex envelopes and provide counterexamples demonstrating that\, in general\, stability fails. Next\, we investigate a class of models where the indifference price does not depend on the preferences or the initial wealth. Here\, under the existence of an equivalent separating measure\, in the settings of deterministic preferences\, we show that the class of indifference price invariant models is the class of models where the dual domain is stochastically dominant of the second order. We also provide a counterexample showing that\, in general\, this result does not hold over stochastic preferences\, where instead\, we show that the indifference price invariant models are complete models (in both small and large markets). In the process\, we establish a theorem of independent interest on the stability of the optimal investment problem under perturbations of preferences. Our results are new in both small and large markets\, and thus\, in particular\, we introduce large stochastically dominant models\, give examples of such models\, and characterize them as the indifference price invariant ones over deterministic preferences.
UID:110937-21825884@events.umich.edu
URL:https://events.umich.edu/event/110937
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 1360
CONTACT:
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BEGIN:VEVENT
DTSTAMP:20240202T161524
DTSTART;TZID=America/Detroit:20240313T160000
DTEND;TZID=America/Detroit:20240313T170000
SUMMARY:Workshop / Seminar:Generalization of Shapley's cooperative value allocation theory via random coalition process
DESCRIPTION: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.\n\nWe 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.
UID:114233-21832531@events.umich.edu
URL:https://events.umich.edu/event/114233
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 1360
CONTACT:
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20240202T161732
DTSTART;TZID=America/Detroit:20240320T160000
DTEND;TZID=America/Detroit:20240320T170000
SUMMARY:Workshop / Seminar:Democratizing or Demoralizing: The Impact of Robinhood on Trading Costs and Volatility
DESCRIPTION: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.
UID:110936-21825883@events.umich.edu
URL:https://events.umich.edu/event/110936
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 1360
CONTACT:
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BEGIN:VEVENT
DTSTAMP:20240205T154353
DTSTART;TZID=America/Detroit:20240327T160000
DTEND;TZID=America/Detroit:20240327T170000
SUMMARY:Workshop / Seminar:Non-parametric estimations for graphon mean-field particle systems
DESCRIPTION:We consider the graphon mean-field system introduced by Bayraktar et al. in Bayraktar\, Chakraborty\, Wu (AAP 2023)\n which is the large-population limit of a heterogeneously interacting diffusive particle system.\n The interaction is of mean-field type with weights characterized by an underlying graphon function.\n Via continuous observations of the trajectories of the finite-population particle system\,\n we build plug-in estimators of the particle densities\, drift coefficients\, and graphon interaction weights of the mean-field system. \n 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\n 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. \n 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. \n\nJoint work with Erhan Bayraktar
UID:118407-21841044@events.umich.edu
URL:https://events.umich.edu/event/118407
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 1360
CONTACT:
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BEGIN:VEVENT
DTSTAMP:20230918T104424
DTSTART;TZID=America/Detroit:20240403T160000
DTEND;TZID=America/Detroit:20240403T170000
SUMMARY:Workshop / Seminar:Mean-Field Games for Scalable Computation and Diverse Applications
DESCRIPTION: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).
UID:111486-21827175@events.umich.edu
URL:https://events.umich.edu/event/111486
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 1360
CONTACT:
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20231102T161932
DTSTART;TZID=America/Detroit:20240410T160000
DTEND;TZID=America/Detroit:20240410T170000
SUMMARY:Workshop / Seminar:TBA
DESCRIPTION:TBA
UID:114835-21833674@events.umich.edu
URL:https://events.umich.edu/event/114835
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 1360
CONTACT:
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20240202T161817
DTSTART;TZID=America/Detroit:20240417T160000
DTEND;TZID=America/Detroit:20240417T170000
SUMMARY:Workshop / Seminar:Utilizing game theory and deep learning to find optimal policies for large number of agents
DESCRIPTION: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.
UID:112183-21828569@events.umich.edu
URL:https://events.umich.edu/event/112183
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 1360
CONTACT:
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