Tentative Schedule

Friday, October 24, 2025 

Scott Hall, Bosch Spark Conference Room (5th floor)

8:30 – 9:00 am Registration & Coffee

9:00 – 9:10 am Welcome

9:10 – 10:00 am Mete Soner

10:00 – 10:30 am Xin Zhang

10:30 – 11:00 am Coffee Break

11:00 – 11:30 am Jiamin Jian

11:30 am – 12:00 pm Poster Lightning Talks

12:00 – 12:05 pm Group Photo

12:05 – 2:00 pm Lunch (participants on their own)

2:00 – 2:30 pm Xiaofei Shi

2:30 – 3:00 pm Fang Rui Lim

3:00 – 3:30 pm Coffee Break

3:30 – 4:20 pm Daniel Lacker

4:30 – 6:30 pm Poster Session & Networking (Scott Hall 6142, 6th floor)

Saturday, October 25, 2025 

Scott Hall, Bosch Spark Conference Room (5th floor)

8:40 – 9:10 am Registration & Coffee

9:10 – 10:00 am Sebastian Jaimungal

10:00 – 10:30 am Max Reppen

10:30 – 11:00 am Coffee Break

11:00 – 11:30 am Silvana Pesenti

11:30 am – 12:00 pm Yuqiong Wang

12:00 – 2:00 pm Lunch (participants on their own)

2:00 – 2:30 pm Valentin Tissot-Daguette

2:30 – 3:00 pm Ali Kara

3:00 – 3:30 pm Coffee Break

3:30 – 4:20 pm Ioannis Karatzas

Poster Session on Friday, October 24, 2025 (Scott Hall 6142, 6th floor)

Munawar Ali

Title: Branched Signature Model
Abstract: In this paper, we introduce the branched signature model, motivated by the branched rough path framework of [Gubinelli, Journal of Differential Equations, 248(4), 2010], which generalizes the classical geometric rough path. We establish a universal approximation theorem for the branched signature model and demonstrate that iterative compositions of lower-level signature maps can approximate higher-level signatures. Furthermore, building on the extension method of [Hairer-Kelly. Annales de l'Institue Henri Poincar\'e, Probabilit\'es et Statistiques 51, no. 1 (2015)], we show how to extend the original paths into higher-dimensional spaces via a map $\Psi$, so that the branched signature can be realized as the classical geometric signature of the extended path. This framework not only provides an efficient computational scheme for branched signatures but also opens new avenues for data-driven modeling and applications.

 Guillermo Alonso Alvarez

Title: Contracting a crowd of heterogeneous agents

Abstract: We study a principal-agent model that involves a large population of heterogeneously interacting agents. By extending the existing methods, we find the optimal contracts assuming a continuum of agents, and show that, when the number of agents is sufficiently large, the optimal contracts for the problem with a continuum of agents are near-optimal for the finite agents problem. We make comparative statics and provide numerical simulations to analyze how the agents’ connectivity affects the principal’s value, the effort of the agents, and the optimal contracts.

Manuel Arnese

Title: Sharp propagation of chaos for mean field langevin dynamics and mean field games

Abstract: We establish the sharp rate of propagation of chaos for McKean--Vlasov equations with coefficients that are non-linear in the measure argument; we then apply our results to Wasserstein gradient flows and mean field games. Our arguments combine a version of the BBGKY hierarchy with ideas from the literature on weak propagation of chaos and analysis on the space of measures.

Sunday Timileyin AYODEJI

Title: Applications of Shapley Value to Financial Decision-Making and Risk Management

Abstract: We investigate the application of the Shapley value in addressing risk-related challenges, focusing on two primary areas. The first area explores the role of the Shapley value in the financial sector, specifically in managing portfolio risk. By conceptualizing a portfolio of assets as a cooperative game, we analyze the contribution of individual securities to the reduction in overall portfolio risk. The second area addresses emergency facility logistics, where the Shapley value is utilized to optimize the selection of potential facility locations and mitigate the risks associated with the storage and transportation of hazardous materials. Using Markowitz’s mean-variance framework, the Shapley value facilitates a fair and efficient allocation of risk across portfolio assets, identifying both risk-increasing and risk-reducing assets. Through numerical experiments, we demonstrate that the Shapley value offers valuable insights into the equitable distribution of financial resources and the strategic placement of facilities to manage systemic risks. These findings highlight the practical advantages of integrating game-theoretic approaches into risk management strategies to enhance fairness, efficiency, and the robustness of decision-making processes.

Christian Fiedler 

Title: From Online Vector Balancing to Mean-Field Stochastic Control”

Abstract: Online vector balancing problems (OVBPs) are a central task in discrepancy theory. Given a finite stream of vectors $v_1,\dots ,v_n\in\mathbb{R}^d$, the goal is to adaptively choose signs $\varepsilon_k\in\{\pm 1\}$ so that the signed sum $\sum_{k=1}^{n}\varepsilon_k v_k$ is small in every coordinate. Such problems have been studied extensively from an algorithmic point of view. We examine the OVBP from the new perspective of stochastic control. Under i.i.d. Gaussian inputs $v_k\sim\mathcal{N}(0,I_d)$ and under the standard scaling $n/d \to T \in (0,\infty)$, we conjecture that the mean-field scaling limit is characterized by a continuous-time stochastic control problem of novel type. In it, one steers a Brownian motion with an $L^2$‑constrained drift to minimize the $L^\infty$‑norm of the state at the terminal time $T$. We provide strong partial results supporting this convergence. We establish the value of the limiting control problem as a lower bound for the asymptotic value of the OVBP. More significantly, we also show that restricting the limiting problem to a suitable class of controls yields an upper bound on the asymptotic value. This connection suggests new avenues for algorithm design for OVBP based on stochastic control.

Felix Hoefer

Title: Learning Markov Perfect Equilibria in Discrete Games

Abstract: We study dynamic finite-player and mean-field stochastic games within the framework of Markov perfect equilibria (MPE). Unlike their continuous-time analogues, discrete-time finite-player games generally do not admit unique MPE. However, we show that uniqueness is remarkably recovered when the time steps are sufficiently small, and we provide examples demonstrating the necessity of this assumption. This result, established without relying on any monotonicity conditions, underscores the importance of inertia in dynamic games. We leverage the dynamic uniqueness to discuss different learning algorithms and prove their convergence to the unique MPE.

Ka Lok Lam

Title: Feynman Formula for Discrete-time Quantum Walks

Abstract: We explicitly connect (discrete-time) quantum walks on Z with a four-state Markov additive process via a Feynman-type formula. Using this representation, we derive a relation between the spectral decomposition of the Markov additive process

and the limiting density of the homogeneous quantum walk. In addition,  we consider a space-time rescaling of quantum walks, which leads to a system of quantum transport PDEs in continuous time and space with a phase interaction term. Our probabilistic representation of this type of PDE offers an efficient Monte Carlo computational technique.

Ruslan Mirmominov

Title: Convergence of adapted empirical measure under mixing condition

Abstract: We study the convergence of the adapted empirical measure in adapted Wasserstein distance when the observations satisfy certain mixing conditions. We obtain a moment estimate, concentration inequality and consistency results. We also derive general nonasymptotic exponential concentration inequalities for Lipschitz functions of the observations. We include numerical simulations.

Kyunghoo Mun

Title: Phase Transitions and Linear Stability for the mean-field Kuramoto-Daido model

Abstract: We study the McKean-Vlasov equation $$\partial_{t} q = {1 \over 2} \partial_{\theta}^{2} q - K \partial_{\theta}(q \  \partial_{\theta} (W*q)),$$ on the circle $[0, 2\pi]$, where $K>0$ is the interaction strength. The bimodal interaction potential $$W(\theta)=\cos\theta + m \cos 2\theta, \quad m \geq 0,$$ defines the Kuramoto-Daido model, while $m=0$ reduces to the Kuramoto model. 

    We fully characterize the phase transition threshold $K_{c}$ by comparing it to the linear stability threshold $K_\# = \min (1, m^{-1})$ of the uniform distribution. When $m \leq 1/2,$ $K_{c}$ coincides with that of the Kuramoto model, $i.e.$ $K_{c}=1.$ On the other hand, for $m \geq 2,$ we show $K_c= m^{-1}.$ Also, we completely identify the regimes in which the phase transition is continuous or discontinuous by the value of $m$. 

    Furthermore, in the supercritical regime $K>1,$ we analyze the linear stability of a non-uniform stationary solution $q,$ which is the unique global minimizer of the free energy \[

        \cF(q) = {1 \over 2} \int q \log (\frac{q}{(2\pi)^{-1}}) d\theta - {K \over 2} \int q (W*q) d\theta.

    \] Our approach extends the Dirichlet form method of  [L. Bertini, G. Giacomin, and K. Pakdaman, \textit{J. Stat. Phys.}, {138} (2010), pp.~270--290] from the Kuramoto model to the Kuramoto-Daido setting. In particular, for $m \leq 4.661 \times 10^{-4},$ when $K>1$, we establish an explicit lower bound on the spectral gap of the linearized McKean-Vlasov operator at $q.$ To our knowledge, this is the first rigorous stability analysis for bimodal interactions.

Jonghwa Park 

Title: On a T_1  Transport inequality for the adapted Wasserstein distance

Abstract: The L^1 transport-entropy inequality (or T_1 inequality), which bounds the 1-Wasserstein distance in terms of the relative entropy, is known to characterize Gaussian concentration. To extend the T_1 inequality to laws of discrete-time processes while preserving their temporal structure, we investigate the adapted T_1 inequality which relates the 1-adapted Wasserstein distance to the relative entropy. Building on the Bolley--Villani inequality, we establish the adapted T_1 inequality under the same moment assumption as the classical T_1 inequality.

Bixing Qiao

Title: A New Approach for the Continuous Time Kyle-Back Strategic Insider Equilibrium Problem

Abstract: This project considers a continuous time Kyle-Back model which is a game problem between an insider and a market marker. The existing literature typically focuses on the existence of equilibrium by using the PDE approach, which requires certain Markovian structure and the equilibrium is in the bridge form. We shall provide a new approach which is used widely for stochastic controls and stochastic differential games. We characterize all equilibria through a coupled system of forward backward SDEs, where the forward one is the conditional law of the inside information and the backward one is the insider's optimal value. In particular, when the time duration is small, we show that the FBSDE is well posed and thus the game has a unique equilibrium. This is the first uniqueness result in the literature, without restricting the equilibria to certain special structure. Moreover, this unique equilibrium may not be Markovian, indicating that the PDE approach cannot work in this case. 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. We show that, although the bridge type of equilibria in the literature does not satisfy the required integrability for our equilibria, its truncation serves as a desired approximate equilibrium and its value belongs to our set value. Finally, we characterize our set value through a level set of certain standard HJB equation.

Emmanuel Siyanbola

Title: Hybrid Transformer–LSTM with Multitask Quantile Learning for Bitcoin Volatility and VaR Forecasting.

Abstract: Cryptocurrency markets such as Bitcoin are well known for their extreme ups and downs, which makes managing financial risk especially challenging. Traditional models, while useful, often struggle to capture the complex patterns in these markets. In this project, I develop a new hybrid deep learning model that combines two powerful approaches—Transformers (which are effective at capturing long-term patterns) and Long Short-Term Memory (LSTM) networks (which specialize in short-term dynamics). The model uses a multitask learning strategy to forecast both overall volatility and Value-at-Risk (VaR), a common measure of extreme losses. The study covers daily Bitcoin data from 2010 to 2025, along with related financial indicators such as the VIX (fear index), the Fear & Greed Index, and blockchain network statistics. The model is trained on historical data and evaluated against several benchmarks: Historical Simulation, GARCH (a widely used econometric model), a standalone LSTM, and a standalone Transformer. To test performance, the model is judged on both accuracy (using measures like mean squared error) and risk reliability (using statistical back tests of VaR). Early findings show that the hybrid model provides more reliable risk forecasts than either traditional econometric models or single deep learning approaches.

This work demonstrates the potential of modern machine learning in financial risk management and highlights how combining different models can improve decision-making in volatile markets like cryptocurrencies.

Andrés Riveros Valdevenito 

Title: Linear Convergence of Gradient Descent for Quadratically Regularized Optimal Transport

Abstract: In optimal transport, quadratic regularization is an alternative to entropic regularization when sparse couplings or small regularization parameters are desired. Here quadratic

regularization means that transport couplings are penalized by the squared L2 norm, or equivalently the χ2 divergence. While a number of computational approaches have been shown to work in practice, quadratic regularization is analytically less tractable than entropic, and we are not aware of a previous theoretical convergence rate analysis. We focus on the gradient descent algorithm for the dual transport problem in the continuous setting. This problem is convex but not strongly convex; its solutions are the potential functions that approximate the Kantorovich potentials of unregularized optimal transport. The gradient descent steps are straightforward to implement, and stable for small regularization parameter—in contrast to Sinkhorn’s algorithm in the entropic setting. Our main result is that gradient descent converges linearly; that is, the L2 distance between the iterates and the limiting potentials decreases exponentially fast. Our analysis focuses on the linearization of the gradient descent operator at the optimum and uses functional-analytic arguments to bound its spectrum. These techniques seem to be novel in this area and are substantially different from the approaches familiar in entropic optimal transport.

Qinxin Yan 

Title: Particle systems with singular interactions on sparse graphs

Abstract: We study particle systems interacting via hitting times on sparsely connected graphs, following the framework of Lacker, Ramanan and Wu. We provide general robustness conditions that guarantee the well-posedness of physical solutions to the dynamics, and demonstrate their connections to the dynamic percolation theory. We then analyze the limiting behavior of the particle systems, establishing the continuous dependence of the joint law of the physical solution on the underlying graph structure with respect to local convergence and studying the convergence of the global empirical measure, which extends the general results by Lacker et al. to systems with singular interactions. The model proposed provides a general mathematical framework in continuous time for analyzing systemic risks in large sparsely connected financial networks with a focus on local interactions, featuring instantaneous default cascades.

Zhouhao Yang

Title: A Two-fold Randomization Framework for Impulse Control Problems

Abstract: We propose and analyze a randomization scheme for a general class of impulse control problems. The solution to this randomized problem is characterized as the fixed point of a compound operator which consists of a regularized nonlocal operator and a regularized stopping operator. This approach allows us to derive a semi-linear Hamilton-Jacobi-Bellman (HJB) equation. Through an equivalent randomization scheme with a Poisson compound measure, we establish a verification theorem that implies the uniqueness of the solution. Via an iterative approach, we prove the existence of the solution. The existence--and--uniqueness result ensures the randomized problem is well-defined. We then demonstrate that our randomized impulse control problem converges to its classical counterpart as the randomization parameter \(\blambda\) vanishes. This convergence, combined with the value function's \(\mathcal{C}^{2,\alpha}_{loc}\) regularity, confirms our framework provides a robust approximation and a foundation for developing learning algorithms. Under this framework, we propose an offline reinforcement learning (RL) algorithm. Its policy improvement step is naturally derived from the iterative approach from the existence proof, which enjoys a geometric convergence rate. We implement a model-free version of the algorithm and numerically demonstrate its effectiveness using a widely-studied example. The results show that our RL algorithm can learn the randomized solution, which accurately approximates its classical counterpart. A sensitivity analysis with respect to the volatility parameter \(\sigma\) in the state process effectively demonstrates the exploration--exploitation tradeoff.

Yuyang Zhang

Title: Optimal Contract, Delegated Investment, and Information Acquisition”

Abstract: This paper examines a model of delegated investment within the framework of a noisy rational expectations equilibrium. Portfolio managers can acquire costly signals about asset payoffs but incur portfolio management costs. They receive compensation from delegated investors and make investment decisions on their behalf. The optimal contract includes a benchmark component that mitigates agency frictions arising from portfolio management costs. The precision of private signals chosen by portfolio managers is determined by equilibrium market conditions. Private and public signals substitute. When portfolio management costs increase, both the performance and benchmark components of the optimal contract increase, less private signals are aggregated into the public signal, leading to a worse public price informational efficiency. When a social planner has sufficient concerns on the welfare of direct investors or liquidity providers, the social optimal public price informational efficiency improves comparing to the decentralized economy counterparts.”

Haotian Zong

Title: Cost‐Aware Sequential Testing for Human-in-the-Loop LLM Tasks

Abstract: Large language models (LLMs) underpin applications ranging from automated customer support to machine translation, yet their reliable deployment depends on rigorous evaluation, safety checks, and human-in-the-loop feedback. In practice, each human judgment or safety audit carries a nontrivial cost, arrives at random times, and can yield noisy or even conflicting assessments. Existing methods often rely on fixed sample sizes or static quality thresholds, offering little adaptivity to streaming, costly feedback. We propose a general Bayesian sequential testing framework that models these interactions under uncertainty and cost constraints. Our framework is broadly applicable to a range of LLM-centric tasks, such as annotator performance monitoring, human evaluation of new models, red-teaming for safety testing, and automated data filtering. A key feature of our approach is modeling the arrival of information signals--such as individual human annotations or safety‐audit outcomes--as a Poisson process, capturing the random, noisy dynamics inherent in human-in-the-loop feedback. We derive a diffusion approximation of the tester’s posterior belief over the unknown binary state (e.g.\ annotator reliability or model safety) in a high-frequency, weak-signal regime, and characterize optimal stopping rules that balance misclassification risk against information-acquisition cost. Our results yield interpretable stopping rules and clarify the trade-offs between information precision, acquisition cost, and decision risk in sequential testing environments. Together, these insights provide a practical blueprint for designing adaptive, cost-effective human-in-the-loop evaluation and safety pipelines for LLMs.