A Doubly Continuous Model for Equilibrium Trading Dynamics

In standard rational expectations models with homogeneous agents, differences in information are typically insufficient to generate trade in equilibrium. To address this issue, we introduce and analyze a doubly continuous model with continuous time and a continuous agent space. In this setting, each agent is infinitesimally small and contributes zero to aggregate trade, while collective trading activity emerges from the aggregation over non-negligible sets of agents. The analysis relies on tools from Brownian sheets and multiparameter stochastic calculus, allowing us to explicitly characterize equilibrium prices and trading dynamics in this doubly continuous setting when investors have general risk-averse preferences. The framework provides new insights into how dispersed information and heterogeneous beliefs translate into equilibrium trading, price informativeness, and market activity. 

This talk is based on joint work with Efstathios Avdis (University of Alberta), Sergei Glebkin (INSEAD), and Raphael Huwyler (University of Alberta).

Existence of an equilibrium with limited stock market participation and power utilities

We prove existence and uniqueness of a solution to a singular and path-dependent Riccati-type ODE. As an application, we use the ODE solution to prove existence of a Radner equilibrium with homogenous power-utility investors in the limited participation model from Basak and Cuoco (1998). To ensure that all traders survive in the long run, we conclude by giving a model variation with heterogenous time-preferences.  

This is joint work with Paolo Guasoni (Università di Bologna and Dublin City University), Giovanni Leoni (CMU), and Heeyoung Kwon (Rutgers).

Reinforcement Learning for Entropy-Regularized Stochastic Control with Model Uncertainty

We propose a reinforcement-learning (RL) scheme for solving the entropy-regularized Hamilton–Jacobi–Bellman (HJB) equation arising in stochastic control with model uncertainty. Compared with the standard policy-iteration algorithm (PIA) discussed in our earlier work, our approach overcomes two key limitations: (i) the classical PIA depends on unknown model parameters, rendering it impractical; and (ii) it requires derivatives of the value function, and since an L2 (or uniform) approximation of the value function does not lead to a good approximation of its derivatives, the convergence is not guaranteed. Our method assumes only that the diffusion (volatility) coefficient is known—an empirically reasonable requirement—while allowing the drift to be unknown. The algorithm operates entirely via coupled fixed-point maps that are estimable from simulation and trials without derivative access. We prove convergence and obtain rate of convergence, and we corroborate the theory with comprehensive numerical experiments. As a further illustration, we also extend the algorithm framework into a special case of volatility control in one dimension. 

This talk is based on joint work with Jin Ma, Jianfeng Zhang, and Xunyu Zhou.

Forecasting and Manipulating the Forecasts of Others

When actions reshape opponents' signals, each agent's optimal response depends on an infinite hierarchy of beliefs about beliefs (Townsend, 1983) that has resisted exact analysis for four decades. We resolve this hierarchy by estimating primitive shocks rather than the state, collapsing Nash equilibrium onto a deterministic fixed point in impulse-response maps with no truncation, large-population limit, or exogenous-signal assumption. The characterization produces a shadow price of manipulation, the information wedge, pricing the marginal value of shifting opponents' posteriors. In a two-player benchmark, nearly all welfare gains from pooling information come from eliminating bilateral belief manipulation rather than from improving state estimation. When players differ in efficiency, concentrating precision on the efficient player collapses the manipulation arms race, while arming the inefficient player maximizes bilateral waste. A Kyle–Back embedding extends the framework to strategic trading with asymmetric private learning.

Link to preprint: https://arxiv.org/abs/2603.12140