2022/09/30 by Pierre Carmier, Carmier, Pierre
Decision Sciences · Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #Economic theories and models #FOS: Economics and business #FOS: Mathematics #FOS: Physical sciences #Game Theory and Applications #Probability (math.PR) #Statistical Mechanics (cond-mat.stat-mech) #Trading and Market Microstructure (q-fin.TR)
paper · pdf · doi:10.48550/arxiv.2209.15429
openalex publication_date 2022/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We derive an upper bound for the expected gain of informed traders in the Glosten-Milgrom model with finite horizon, fully analogous to a generalized second law of thermodynamics. This result extends that obtained by Touzo et al. a couple of years ago. The proof relies on Bayesian inference (exploiting the invariance of the problem under consecutive game sequences) and an interesting entropic inequality. We also provide numerical results both supporting the existence of a characteristic timescale in the model and illustrating the magnitude of gain fluctuations. Other possible extensions are discussed.