Paper: arXiv 2501.03658

Abstract

We characterise the solutions to a continuous-time optimal liquidity provision problem in a market populated by informed and uninformed traders. In our model, the asset price exhibits fads – these are short-term deviations from the fundamental value of the asset. Conditional on the value of the fad, we model how informed traders and uninformed traders arrive in the market. The market maker knows of the two groups of traders but only observes the anonymous order arrivals. We study both, the complete information and the partial information versions of the control problem faced by the market maker. In such frameworks, we characterise the value of information, and we find the price of liquidity as a function of the proportion of informed traders in the market. Lastly, for the partial information setup, we explore how to go beyond the Kalman-Bucy filter to extract information about the fad from the market arrivals.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper is heavy on advanced stochastic control and filtering theory (e.g., solving HJB equations, Kalman-Bucy filters) but presents no empirical backtests, code, or specific data implementations, focusing instead on theoretical characterization and sensitivity analysis via simulations.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Characterize optimal liquidity provision<br>in a market with informed/uninformed traders<br>and asset price fads"] --> B["Model Setup<br>Data: Arrival processes, asset fundamentals,<br>fad dynamics, informed/uninformed trader proportions"]
  B --> C["Methodology: Two Frameworks<br>1. Complete Information<br>2. Partial Information"]
  C --> D["Computational Process<br>Continuous-time optimal control<br>via stochastic calculus and HJB equations"]
  D --> E["Key Findings<br>• Value of information for market maker<br>• Price of liquidity as function of informed traders<br>• Filtering methods beyond Kalman-Bucy for fads"]

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and 48 more
  1. Optimal investment with a noisy signal of future stock prices — → 2302.10485
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  3. Brokers and informed traders: dealing with toxic flow and extracting trading signals (2025)
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8 of 56 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.