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DTSTART:20070311T020000
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DTSTART:20071104T020000
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BEGIN:VEVENT
DTSTAMP:20260820T232857
DTSTART;TZID=America/Detroit:20260902T160000
DTEND;TZID=America/Detroit:20260902T170000
SUMMARY:Workshop / Seminar:Theory and Methods for Conditional Diffusion Models
DESCRIPTION:will study conditional sampling with diffusion models under linear constraints\, with a focus on understanding how a pre-trained unconditional diffusion model can be used to sample from a conditional distribution. I will present a normal–tangent decomposition of the conditional score that separates the effect of the observed constraints from the remaining uncertainty in the distribution. This decomposition provides a way to characterize the discrepancy between the unconditional and conditional diffusion dynamics\, and to relate this discrepancy to information-theoretic quantities.\n\nBased on this perspective\, I will introduce a sampling method that combines projected Langevin initialization on the constraint set with guided reverse diffusion. I will discuss theoretical and information-theoretic guarantees for the resulting sampler\, as well as numerical results illustrating its behavior on linear inverse problems. At the end\, I will also briefly discuss related results showing how the information content and structural properties of a target distribution can reduce the dependence of diffusion sampling on the ambient dimension.
UID:150579-21909651@events.umich.edu
URL:https://events.umich.edu/event/150579
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 1360
CONTACT:
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20260803T153429
DTSTART;TZID=America/Detroit:20260909T160000
DTEND;TZID=America/Detroit:20260909T170000
SUMMARY:Workshop / Seminar:Stability\, Approximation\, and Robustness of Optimal Policies in POMDPs
DESCRIPTION:In this talk\, I will focus on the stability\, approximation\, and robustness of optimal policies in partially observable Markov decision processes (POMDPs) under discounted and average cost criteria.\n\nI will begin with filter kernel perturbation under model change. I will establish how small perturbations in the transition or observation kernels lead to explicit\, nonasymptotic bounds on both the filter kernel and the performance of the induced policies. A primary result demonstrates that an optimal policy computed under an incorrect model remains near optimal for the true model\, with quantitatively bounded errors.\n\nBuilding on these stability concepts\, I will then talk about the average cost setting and describe conditions under which the nonlinear filter exhibits a contraction property. Under these conditions\, the vanishing discounted approach yields a solution to the average cost optimality equation\, guaranteeing the existence of a stationary optimal policy. Furthermore\, this provides explicit bounds that quantify the influence of initial prior distribution errors and model errors on long run performance.\n\nFinally\, I will present results on implementable approximations. I will introduce refined error bounds for finite window controllers and conclude by discussing how Q learning can be utilized through either finite window or the quantization of the belief process to obtain near optimal policies for both discounted and average cost criteria.
UID:149581-21906722@events.umich.edu
URL:https://events.umich.edu/event/149581
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 1360
CONTACT:
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20260803T142311
DTSTART;TZID=America/Detroit:20260916T160000
DTEND;TZID=America/Detroit:20260916T170000
SUMMARY:Workshop / Seminar:Optimal Contract\, Delegated Investment\, and Information Acquisition
DESCRIPTION:We study a model of delegated investment within a noisy rational expectations equilibrium framework. Portfolio managers can acquire costly private information about asset payoffs but incur portfolio management costs\, and are compensated by investors to make investment decisions on their behalf. We show that the optimal contract features a benchmark component that mitigates the agency frictions arising from portfolio management costs. The precision of managers' private information is determined endogenously in market equilibrium\, with private and public information acting as substitutes. As portfolio management costs increase\, both the performance-based and benchmark components of the optimal contract become more sensitive to investment outcomes\, while fewer private signals are incorporated into prices\, reducing market informational efficiency. We further show that when a social planner places sufficient weight on the welfare of direct investors and liquidity providers\, the socially optimal equilibrium achieves greater price informational efficiency than the decentralized equilibrium. The talk will focus on the interaction between optimal contracting\, information acquisition\, and market efficiency\, together with the economic intuition underlying these results.
UID:149582-21906724@events.umich.edu
URL:https://events.umich.edu/event/149582
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 1360
CONTACT:
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20260727T104702
DTSTART;TZID=America/Detroit:20260923T160000
DTEND;TZID=America/Detroit:20260923T170000
SUMMARY:Workshop / Seminar:Buying Time: Optimal Service Purchase and Retirement Timing in Defined Benefit Plans
DESCRIPTION:We study retirement timing decisions in a defined benefit (DB) pension plan with a service-purchase\noption. An employee who would otherwise retire at a fixed time T may elect to purchase L additional\nyears of service and retire early. Earlier retirement provides additional leisure but requires an upfront\npayment and typically results in a reduced post-retirement income stream. We model this trade-off in\na continuous-time retirement framework by allowing the employee to choose L to maximize the value\nof wealth and leisure at retirement in both deterministic and life-contingent settings. Our model\ncaptures a common feature of public pension systems: early retirement is often accompanied by both\nan upfront cost and a permanent reduction in benefits. We show that this structure yields tractable\nand intuitive results in several benchmark cases\, including settings without mortality risk and settings\nwith mortality risk under simplifying assumptions. In more general cases\, we characterize optimal\nbehavior through comparative statics and numerical examples. A key insight is that the interaction\nbetween the finite-horizon value of leisure and the lifetime cost embedded in pension pricing can\ngenerate a range of behaviors\, including monotone strategies and interior optima. While many results\nalign with economic intuition\, others require more careful interpretation. We also extend the model to\nallow for dynamic decision-making via a multi-period service-purchase option\, solved by backward\ninduction. The results provide insight into optimal retirement timing and the role of plan design in\nshaping participant behavior. This is joint work with David Kausch and Virginia Young.
UID:149578-21906720@events.umich.edu
URL:https://events.umich.edu/event/149578
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 1360
CONTACT:
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20260729T153011
DTSTART;TZID=America/Detroit:20260930T160000
DTEND;TZID=America/Detroit:20260930T170000
SUMMARY:Workshop / Seminar:Quantitative propagation of chaos and universality for asymmetric Langevin spin glass dynamics
DESCRIPTION:We obtain quantitative estimates on quenched propagation of chaos for Langevin spin glass dynamics with i.i.d. disorder. Prior work in the case of Gaussian disorder established the qualitative convergence of the law of a single spin to a deterministic McKean--Vlasov limit. We prove convergence rates in expected Wasserstein distance and quantitative concentration rates for Lipschitz observables under the assumption that the disorder satisfies the T_2 inequality. The proof uses a coupling argument\, together with techniques from concentration of measure\, filtering theory\, and Malliavin calculus.
UID:149663-21906910@events.umich.edu
URL:https://events.umich.edu/event/149663
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 1360
CONTACT:
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20260407T124520
DTSTART;TZID=America/Detroit:20261007T160000
DTEND;TZID=America/Detroit:20261007T170000
SUMMARY:Workshop / Seminar:Robust and Risk-Sensitive Acceleration in Gradient Methods
DESCRIPTION:First-order methods such as gradient descent (GD) are foundational in optimization. In unconstrained problems with exact gradients\, momentum-based methods—most notably Nesterov’s accelerated gradient descent (AGD) and Polyak’s heavy-ball (HB) method—achieve faster convergence by improving dependence on the condition number. However\, this acceleration comes at a cost: momentum amplifies gradient noise\, making these methods less robust than GD under standard parameter choices and requiring more accurate gradient estimates to attain comparable accuracy. Similar challenges arise in convex and nonconvex min–max optimization.\nMotivated by applications in machine learning\, this talk studies unconstrained and min–max optimization under deterministic\, unbiased stochastic\, and biased stochastic gradient noise. I will present new algorithms that achieve optimal robustness against different noise types\, using control-theoretic tools such as the H_2​ norm\, the H_∞​ norm\, and the risk-sensitivity index\, together with coherent risk measures. I will also discuss worst-case noise constructions and high-probability convergence guarantees. This perspective builds a bridge between optimization and robust control theory and enables the design of noise-robust and risk-sensitive accelerated methods.\nRepresentative Publications:\nM. Gürbüzbalaban\, Y. Syed\, N. S. Aybat\, Accelerated gradient methods with biased gradient estimates: Risk sensitivity\, high-probability guarantees\, and large deviation bounds\, Journal of Nonlinear and Variational Analysis\, 2026 (Special Issue). https://jnva.biemdas.com/archives/2927\nM. Gürbüzbalaban\, Robustly Stable Accelerated Momentum Methods with a Near-Optimal L_2​ Gain and H_∞​ Performance\, Mathematics of Operations Research\, 2025.\nhttps://pubsonline.informs.org/doi/abs/10.1287/moor.2023.0321\nB. Can and M. Gürbüzbalaban\, Entropic risk-averse generalized momentum methods\, Optimization Methods and Software\, 2025. https://www.tandfonline.com/doi/abs/10.1080/10556788.2025.2549356
UID:141373-21888712@events.umich.edu
URL:https://events.umich.edu/event/141373
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 1360
CONTACT:
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20260810T083123
DTSTART;TZID=America/Detroit:20261014T160000
DTEND;TZID=America/Detroit:20261014T170000
SUMMARY:Workshop / Seminar:Kullback–Leibler Mirror-Prox for Measure-Valued Variational Inequalities and Mean-Field Equilibria
DESCRIPTION:We study the computation of static mean-field equilibria on a compact state space by formu-\nlating the equilibrium condition as a variational inequality over probability measures. We propose\nan entropic variant of Korpelevich’s extragradient algorithm—the Kullback–Leibler Mirror-Prox\nmethod—in which Euclidean projections are replaced by relative-entropy proximal steps. Each\nhalf-step is therefore an explicit exponential reweighting of the current measure\, implemented on a\nfinite state-space discretization. Under Lasry–Lions monotonicity and continuity assumptions\, we\nprove convergence of mesh-refined ergodic averages and obtain finite-iteration Minty-residual and\napproximate-equilibrium bounds that jointly quantify iteration and discretization errors. Under\nstrong monotonicity\, we derive metric convergence rates for the last\, best\, and averaged iterates.\nWe also develop a KL-type Tikhonov regularization that selects the equilibrium minimizing relative\nentropy with respect to a reference measure. The framework applies to potential and nonpotential\ncost operators and does not require differentiability or convexity of the cost in the individual state.\n\nJoint work with Erhan Bayraktar\, Ibrahim Ekren and Lu Vy.
UID:150040-21907900@events.umich.edu
URL:https://events.umich.edu/event/150040
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 1360
CONTACT:
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20260608T221120
DTSTART;TZID=America/Detroit:20261028T160000
DTEND;TZID=America/Detroit:20261028T170000
SUMMARY:Workshop / Seminar:TBA
DESCRIPTION:TBA
UID:148617-21904532@events.umich.edu
URL:https://events.umich.edu/event/148617
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 1360
CONTACT:
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20260807T155844
DTSTART;TZID=America/Detroit:20261104T160000
DTEND;TZID=America/Detroit:20261104T170000
SUMMARY:Workshop / Seminar:Exploratory Optimal Reinsurance under the Mean-Variance Criterion
DESCRIPTION:This paper proposes a Reinforcement Learning (RL) approach to the optimal reinsurance problem\nwhen the insurer faces uncertainty about the insurance claim dynamics. To this end\, we first formulate\nan exploratory version of the problem as a relaxed stochastic control problem. Within a broad class of\nparametric retention functions and general risk loading functions\, we derive the closed-form equilibrium\npolicy under the continuous-time mean-variance criterion. This is achieved through a formal verification\ntheorem and solving classical solutions of a system of exploratory extended Hamilton-Jacobi-Bellman\n(EEHJB) equations. We then establish a policy iteration theorem\, showing that starting from any timeand state-homogeneous policy\, policy iteration converges to the derived equilibrium policy. Next\, we\ndevelop a martingale orthogonality theorem\, which serves as the foundation of our RL algorithm. The\nalgorithm is evaluated through simulation studies and real data from the U.S. National Flood Insurance\nProgram. Results demonstrate that the RL approach effectively learns unknown claim distributions\,\ntracks unobserved changes in claim dynamics and produces higher insurer surplus trajectories than the\nmaximum likelihood estimation (MLE) approach while simultaneously exhibiting greater robustness to\nthe choice of training window.
UID:150012-21907810@events.umich.edu
URL:https://events.umich.edu/event/150012
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 1360
CONTACT:
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20260819T202729
DTSTART;TZID=America/Detroit:20261118T160000
DTEND;TZID=America/Detroit:20261118T170000
SUMMARY:Workshop / Seminar:A New Approach for the Continuous Time Kyle-Back Strategic Insider Equilibrium Problem
DESCRIPTION:In this talk\, we consider a continuous-time Kyle-Back model which is a game between an insider and a market maker. The existing literature typically focuses on constructing equilibria with a PDE approach\, which requires certain Markovian structures. We characterize all equilibria through a coupled system of forward-backward SDEs. In particular\, when the time duration is small\, we show that the FBSDE is well-posed\, and therefore the game has a unique equilibrium. Moreover\, this unique equilibrium may be non-Markovian and thus not attainable via the PDE approach. We next study the set value of the game\, which roughly speaking is the set of insider's values over all equilibria and thus is by nature unique. Finally\, we characterize the set value through a level set of a certain standard HJB equation.\nIn the second part of the talk\, we apply the new approach to the Kyle-Back model with dynamic legal risk and large numbers of noise traders. In this setting\, the insider chooses a strategy that conceals his identity within a large volume of surrounding trades and concentrates on medium-sized trades.  We establish an intensity-based mathematical framework for explaining the interconnections between insider trading and stealth trading. When the number of noise traders becomes large\, the price impact of the insider asymptotically vanishes\, and consequently the stochastic game becomes deterministic optimizations\, which also carry implications for regulatory investigations and sanctions.\n\nThe results above include the joint work with Weixuan Xia and with Jianfeng Zhang.
UID:149579-21906721@events.umich.edu
URL:https://events.umich.edu/event/149579
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 1360
CONTACT:
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20260727T104513
DTSTART;TZID=America/Detroit:20261202T160000
DTEND;TZID=America/Detroit:20261202T170000
SUMMARY:Workshop / Seminar:TBA
DESCRIPTION:TBA
UID:149576-21906718@events.umich.edu
URL:https://events.umich.edu/event/149576
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 1360
CONTACT:
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20260727T104405
DTSTART;TZID=America/Detroit:20261209T160000
DTEND;TZID=America/Detroit:20261209T170000
SUMMARY:Workshop / Seminar:THE HEREDITARY LAWS OF LARGE NUMBERS
DESCRIPTION:The celebrated theorem of Komlos (1967) establishes L^1-boundedness as a sufficient condition for a sequence of measurable functions on a probability space to contain a subsequence along which\, and along whose every further subsequence (“hereditarily”)\, the Cesaro averages converge to a “randomized mean” in the spirit of the Strong law of Large Numbers. We provide conditions not only sufficient\, but also necessary\, for this result\, as well as for the hereditary analogues of the Weak Law of Large Numbers\, of the Hsu-Robbins-Erdos Law of Large Numbers\, and of the Law of the Iterated Logarithm. \n\nJoint work with I. Berkes (Budapest) and W. Schachermayer (Vienna).
UID:149577-21906719@events.umich.edu
URL:https://events.umich.edu/event/149577
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics,Statistics
LOCATION:East Hall - 1360
CONTACT:
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20260807T120756
DTSTART;TZID=America/Detroit:20270217T160000
DTEND;TZID=America/Detroit:20270217T170000
SUMMARY:Workshop / Seminar:The optimal rate of convergence in mean field control
DESCRIPTION:I will discuss the sharp rate of convergence of the value functions of N-particle stochastic control problems to their mean field limit\, for merely Lipschitz mean field costs. For d ≥ 2\, the optimal rate is that of the empirical measures of i.i.d. samples in the 1-Wasserstein distance\, as conjectured by Daudin\, Delarue\, and Jackson\, and it persists with additive common noise. In dimension one\, this benchmark can surprisingly be beaten: cooperating particles outperform independent samples\, and the optimal exponent is 4/7\, strictly between the accuracy of independent sampling (N^{-1/2}) and that of quantization (N^{-1}). The proofs rely on a new control-theoretic technique of recoupled shadow flows and\, in dimension one\, on a Gibbs law implementing the cooperation and a Schrödinger ground-state estimate.
UID:149994-21907791@events.umich.edu
URL:https://events.umich.edu/event/149994
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 1360
CONTACT:
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