Schedule for Fall 2026

Speaker: Graeme Baker (Columbia University)

Title: Traveling Waves in Equity Markets with Rank-Based Entry and Exit

Abstract: We model equity markets using geometric Brownian particles entering and exiting at rank-dependent intensities. In the many-firm limit, the capital distribution converges uniformly to the solution of a reaction-diffusion equation with reaction term built from the intensities. Calibrated on CRSP data, the reaction term is bistable, and the long-run capital distribution is a traveling wave: we prove existence, uniqueness, and, for constant coefficients, exponential relaxation. Turnover, not drift, stabilizes the calibrated market. With volatility measured rank by rank, the wave tracks the empirical capital distribution in every decade, determines the capitalization growth of diversity-weighted portfolios, and places the market of the past 50 years just inside the boundary of the diverse phase. Turnover reclaims most of what rebalancing gains. Joint work with Caroline Smyth (Columbia College Class of 2026). Preprint: https://arxiv.org/abs/2608.27156

Speaker: Robert Boyce (Imperial)

Title: Passive impact and internalisation in market making

Abstract: Modern algorithmic market making faces an inherent trade-off between risk management and various forms of market impact. We first derive a model of passive market impact from microscopic principles that can be solved in closed form. Moreover, dealers in the FX market increasingly offer access to internal liquidity pools, which, in addition to providing clients with an alternative means of execution, can create further opportunities for risk management. We proceed to model and investigate these opportunities and observe that passive impact arises endogenously in such a model. These models are calibrated with FX and equities market data.

Speaker: Luhao Zhang (Johns Hopkins)

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.

Speaker: Neil Chriss (Fixed Point Advisors

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Speaker: Soumik Pal (University of Washington)

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Speaker: Marko Weber (NUS)

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Speaker:  Xuedong He (CUHK)

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