We show that net demand for liquidity by algo strategies is identifiable from its trade and price history alone, with no knowledge of its signal or optimization problem. An exact multi-period regret decomposition implies that the sign of this statistic classifies a linear strategy as a net liquidity consumer or provider, recovering the Kyle (1985) informed-trader/market-maker dichotomy from observables alone. Under an AR(1) cost process, the same statistic equals the product of strategy size and the squared Roll (1984) implied spread, making the correction a direct proxy for prevailing illiquidity. Extending to endogenous price impact and aggregating across N correlated strategies yields a liquidity-balance condition whose violation produces welfare loss scaling as N squared, a closed-form fire-sale externality. We calibrate to CRSP equity data (2016-2025), tracking implied spreads through the COVID-19 and 2022 rate-shock episodes, with an estimator computable in O(Tnd) time.
We propose the first deep learning algorithm, the Certainty Equivalent Learning (CEL) algorithm, for solving high-dimensional discrete-time dynamic programming problems with recursive utility. Dynamic programming with recursive utility is numerically challenging because the recur…
Building on the identity that expected regret equals the covariance between costs and decisions, this paper develops the complete derivative theory of the covariance regret functional. We derive the Gâteaux derivative, showing that the universal steepest-descent direction is the…
This paper proposes the certainty-equivalent first-order learning (CEFOL) algorithm, a deep learning algorithm for solving discrete-time dynamic programming problems with recursive utility. Dynamic programming with recursive utility is challenging because nonlinear certainty equi…
A specialist tolerates blind spots that a generalist does not. Usually this is treated as a cost to be minimized. We treat it as a design variable: a deficiency can be kept because it pays and removed on demand in the rare situation where it would be fatal, by routing to a compen…
We address fundamental challenges in representing and computing $\mathbb{R}^{d}$-valued predictable square-integrable processes over $[0,T]$, collected in the space $\mathcal{H}^2_T(\mathbb{R}^{d})$. These processes are central to continuous-time stochastic control, reinforcement…
We propose one-step and two-step methods for policy learning with retrieval-augmented generation (RAG). We formulate RAG-based action selection under the potential outcome framework. In the two-step method, vector search retrieves action-specific neighboring evidence in an embedd…