Abstracts of Talks

Xunyu Zhou

Title: Dynamic Mean–Variance Portfolio Selection with No-Shorting Constraints and Unknown Investment Opportunity Sets

Abstract: We study continuous-time mean–variance portfolio selection with no-shorting constraints and unknown investment opportunity sets from a reinforcement learning (RL) perspective. The problem is a constrained stochastic linear–quadratic control problem for which the entropy-regularized exploratory formulation of Wang et al. (2020) leads to difficulty in theoretical analysis, because enforcing the constraint on the support of randomized policies nullifies the tractable Gaussian exploration. To tackle this challenge, we introduce an auxiliary exploratory problem without entropy in which exploratory policies are still Gaussian whose samples may violate the no-shorting requirement but their means satisfy it. We then prove that, for a suitable choice of exploration variance, the mean of the optimal Gaussian policy of the auxiliary problem coincides with the optimal policy of the original problem. Motivated by this theoretical result, we develop a model-free RL algorithm that learns the optimal policy of the auxiliary (and hence the original) problem directly from trajectory data without estimating the investment opportunity set. A numerical example demonstrates the performance of the proposed algorithm. Joint work with Xun Li and Yutian Wang.

Qi Feng

Title: Langevin Dynamics Based Continuous Policy and Value Iteration for Stochastic Control

Abstract: We introduce a continuous policy-value iteration algorithm where the approximations of the value function of a stochastic control problem and the optimal control are simultaneously updated through Langevin-type dynamics. This framework applies to both the entropy-regularized relaxed control problems and the classical control problems, with infinite horizon. We establish policy improvement and demonstrate convergence to the optimal control under the monotonicity condition of the Hamiltonian. By utilizing Langevin-type stochastic differential equations for continuous updates along the policy iteration direction, our approach enables the use of distribution sampling and non-convex learning techniques in machine learning to optimize the value function and identify the optimal control simultaneously. Numerical experiments are presented for LQ model with a non-concave reward, and a non-LQ example with a skewed-Laplace optimal control.

Pietro Bini

Title: A Beautiful Mind, or Many? Group Deliberation and Strategic Behavior in AI

Abstract: Does group deliberation help AI agents develop more strategic behavior? We compare individual agents with groups built from the same underlying model that deliberate toward a common decision in repeated Beauty Contest and Limit Pricing games. Groups more often reach and sustain strategic behavior and beat individuals in later rounds of direct competition. What differs in how groups and individuals form their choices? Fitting a learning model, we find that groups’ choices give greater weight to recent payoff information and discount older experience faster. We then examine the arguments agents articulate before deciding and their relationship to subsequent actions. Groups more frequently reason about equilibrium and opponents’ behavior, and choices preceded by such strategic reasoning are more likely to be strategic. Together, these findings show that group deliberation promotes the emergence and persistence of strategic behavior in AI agents.

Guanting Chen

Title: Lean-Nexus: Scaling AI-for-Math to Real-World Mathematical Verification

Abstract: Recent AI-for-Math systems perform well on clean benchmarks but struggle with real-world mathematical documents containing implicit assumptions, heterogeneous notation, long dependency chains, and subtle errors. We introduce Lean-Nexus, an agentic framework for understanding, formalizing, and verifying research-level mathematics directly from LaTeX or PDF. Lean-Nexus iteratively performs interpretation, decomposition, formalization, verification, diagnosis, and repair, allowing it to distinguish formalization mismatches from genuine logical issues. It also produces structured reasoning artifacts, including proof dependencies, error annotations, repair trajectories, and verifier feedback. Experiments on research papers show that Lean-Nexus can identify subtle issues and suggest meaningful corrections, demonstrating a practical path toward scaling AI-for-Math from curated benchmarks to real-world mathematical research.

Anran Hu

Title: Dynamic Portfolio Optimization under CVaR Constraints

Abstract: We study continuous-time dynamic portfolio optimization under a Conditional Value-at-Risk (CVaR) constraint on the investor’s terminal loss. For a general class of convex trading objectives, we exploit the auxiliary-threshold representation of CVaR to establish the existence of an optimal strategy and strong duality without requiring market completeness. These results motivate a dual-based nested bisection–golden-search algorithm over the threshold and Lagrangian multiplier, where the inner iterations reduce to standard unconstrained stochastic control problems. We prove that the resulting strategies converge to the optimal control as the number of iterations tends to infinity. Numerical experiments recover the Merton policy when the risk constraint is nonbinding. When the constraint is binding, the optimal strategy becomes state dependent: the investor reduces risky exposure following adverse outcomes but preserves, and near maturity may increase, exposure following favorable outcomes. Thus, a terminal CVaR constraint produces an asymmetric reallocation across states rather than uniform de-risking. Nontraded endowment risk amplifies the conservative adjustment, whereas price impact lowers desired positions and adjustment speeds.

Valentin Tissot-Daguette

Title: Pricing with Passion: The Local Occupied Volatility (LOV) Model

Abstract: We study the Local Occupied Volatility (LOV) model that sits between Dupire’s local volatility and fully path-dependent dynamics. By design, the LOV model ensures automatic calibration to European vanilla options, while offering the flexibility to capture stylized facts of volatility or fit additional instruments. This is achieved via Markovian expansions and the tuning of the so-called occupation sensitivity function that quantifies the effect of path-dependent shocks on volatility. We validate the model through the joint American-European calibration of vanilla options on non-dividend paying stocks.

Ronnie Sircar

Title: Negative Oil: A Feedback Model for Extreme Commodity Futures Prices

Abstract: On April 20, 2020, the May front-month WTI oil futures contract, one day before its expiration date, opened near $17/barrel and dropped far below zero in a single trading day, reaching an intraday low of -$40.32 and settling at -$37.63. This market behavior was unforeseen at the time. We develop a feedback model that operates on top of any standard valuation framework used for pricing commodity futures contracts. The distortion in price is generated by a roll-option instrument which is valued from a nonlinear partial differential equation. We show that the nonlinear PDE can be reduced by one dimension, and that the reduced equation is the Margrabe equation with its variance multiplied by a value-dependent factor generated by the feedback. Numerical solutions demonstrate the model as an explanatory mechanism for the negative oil episode, as well as its mirror image: the LME Nickel short squeeze of March 7-8, 2022 (discussed in a student's poster).

Erhan Bayraktar

Title: Analytical Approach to Continuous-Time Causal Optimal Transport 

Abstract: We study causal optimal transport in continuous time, with Markovian cost, between a finite-state Markov source and a diffusion target. By replacing the source with its conditional law given the observation of the target, we characterize the value of this transport problem through a fully nonlinear parabolic master equation on an enlarged state space. We further show that this value coincides with those of two equivalent stochastic control problems on the simplex: a control of the Kushner--Stratonovich filtering equation with a zero-mean condition, and a state-constrained stochastic optimal control problem. Both formulations give rise to implementable numerical schemes that approximate the value from above and below.

Luhao Zhang

Title: Schrödinger Bridge with Transport Relaxation

Abstract: Motivated by modern machine learning applications where we only have access to empirical measures constructed from finite samples, we relax the marginal constraints of the classical Schrödinger bridge problem by penalizing the transport cost between the bridge's marginals and the prescribed marginals. We derive a duality formula for this transport-relaxed bridge and demonstrate that it reduces to a finite-dimensional concave optimization problem when the prescribed marginals are discrete and the reference distribution is absolutely continuous. We establish the existence and uniqueness of solutions for both the primal and dual problems. Moreover, as the penalty blows up, we characterize the limiting bridge as the solution to a discrete Schrödinger bridge problem and identify a leading-order logarithmic divergence. Finally, we propose gradient ascent and Sinkhorn-type algorithms to numerically solve the transport-relaxed Schrödinger bridge, establishing a linear convergence rate for both algorithms.

Soroosh Shafiee

Title: Mean-Covariance Robust Risk Measurement

Abstract: We introduce a universal framework for mean-covariance robust risk measurement and portfolio optimization. We model uncertainty in terms of the Gelbrich distance on the mean-covariance space, along with prior structural information about the population distribution. Our approach is related to the theory of optimal transport and exhibits superior statistical and computational properties than existing models. We find that, for a large class of risk measures, mean-covariance robust portfolio optimization boils down to the Markowitz model, subject to a regularization term given in closed form. This includes the finance standards, value-at-risk and conditional value-at-risk, and can be solved highly efficiently.

Yu An

Title: An Arbitrage Foundation for Demand Effects in Asset Pricing

Abstract: Trading demand for one asset can move every other price, creating an N*N impact matrix across N assets. This paper provides a practical recipe for estimating those impacts. Starting from no arbitrage, I introduce an axiom that is necessary and sufficient to collapse the system to an N-parameter factor representation. A unique set of canonical factors, mutually uncorrelated in payoffs and in trading demand, ensures that demand for each factor moves only its own price of risk. The resulting factor slopes measure substitution along each factor and, together with no-arbitrage, recover cross-substitution among the underlying assets. These slopes can be estimated factor by factor using instrumented time-series variation, addressing recent concerns about contamination from cross-impacts in demand-based estimation. Equal slopes across factors reproduce the mean-variance benchmark, while a demand-based APT further compresses the system to K<N factor slopes plus one idiosyncratic elasticity.

Gökçe Dayanıklı

Title: Cooperation and Common Pool Resources in Mean Field Games and Extensions with Learning

Abstract: The tragedy of the commons (TOTC) states that individual incentives result in the overuse of common pool resources (CPRs), which may have detrimental future consequences for everyone. However, in many real-life situations this does not occur, and researchers such as Nobel laureate Elinor Ostrom have suggested that mutual restraint by individuals can prevent it. In mean field games (MFGs), since individuals are insignificant and non‑cooperative, TOTC is inevitable. This suggests that MFG models involving CPRs must incorporate both selfishness and altruism to better capture real‑world behavior. Motivated by this, we introduce and analyze equilibrium notions blending cooperative and non‑cooperative actions. We then present a fisheries‑inspired example, discussing theoretical and experimental results. Finally, we address the challenge that understanding intervention policies in mixed MFGs requires knowledge of individuals’ altruism levels, which are generally unobservable. We therefore consider how these levels can be learned from data using inverse learning techniques.

Nathan Sauldubois

Title: Projected McKean--Vlasov Dynamics for Entropic Weak Optimal Transport

Abstract: Unlike classical optimal transport, weak transport costs depend nonlinearly on the conditional law of couplings. This feature is essential in problems involving barycenter, conditional moments, and martingale-type constraints. Meanwhile, such conditional dependence makes ordinary Wasserstein geometry insufficient and calls instead for an adapted Wasserstein viewpoint. In this paper, we investigate the entropy-regularized weak optimal transport via gradient flows in adapted Wasserstein space. We derive, from the formal tangent structure of adapted Wasserstein space and the projection onto the set of couplings with prescribed marginals, a coupled McKean–Vlasov SDE. A novel and subtle term is a projection that, at each Y-location, averages a weak-transport force that already depends on the conditional law of Y given X, thereby preserving marginals while retaining the nonlinear weak-transport structure. Under mild integrability and regularity assumptions, we prove weak existence and uniqueness in law for this projected McKean–Vlasov equation. We then prove that the flow converges, in the adapted Wasserstein topology, to the unique minimizer of the entropic weak optimal transport problem. We also describe a particle approximation and illustrate the dynamics on optimal transport and martingale optimal transport examples.

Melih Iseri

Title: Set-Valued PDEs: Stochastic Control and Games

Abstract: Building upon the dynamic programming principle for set-valued functions arising from many applications, we will present a new notion of set-valued PDEs. The key component is a set-valued Itô formula, characterizing the flows on the surface of the dynamic sets. In the context of multivariate control problems, we establish the well-posedness of the set-valued HJB equations, extending the standard scalar HJB equations to the multivariate setting. As for applications, we first discuss how to construct moving scalarizations, and then how to derive the set-valued PDE for games under Nash equilibria. Additionally, we will explore geometric properties of the solutions and introduce the PDE associated with the corresponding support function. The talk is based on joint work with Jianfeng Zhang and ongoing joint work with Nizar Touzi and Jianfeng Zhang.

Nizar Touzi

Title: New Progress in Continuous Time Principal-Agent Problem

Abstract: We consider the finite horizon continuous-time Principal-Agent problem under deterministic discount factors. Following the Sannikov reduction to a stochastic control problem, we

provide a further characterization of the Principal’s value function in terms of a backward SDE inducing the corresponding optimal contract. In particular, this allows to bypass the fully nonlinear HJB equation satisfied by the Principal value function in the Markovian setting. This new approach allows to handle a new class of Principal-Agent problems which was not accessible with the existing method, namely the setting where the Agent faces a regime-switching control problem.