cs.LGJun 28, 2026

Persona-Trained Monte Carlo: Estimating Market-Outcome Distributions via Swarms of Persona-Conditioned Neural Policy Bots in a Limit Order Book

Authors: Salavat Ishbulatov

Organizations: Independent researcher

Abstract

We propose Persona-Trained Monte Carlo (PTMC), a method for estimating distributions of market-outcome statistics by repeatedly simulating limit-order-book interaction among swarms of persona-conditioned neural-policy trading bots. Each run instantiates many bots sharing one trained policy network but conditioned on heterogeneous, individually sampled persona parameters drawn from a learned trader-heterogeneity distribution; the bots interact in a continuous double auction, and the resulting price path is one Monte Carlo sample. Repeating this over independent persona-population draws yields an ensemble from which a target market statistic is estimated. Randomness enters through persona draws, within-run action sampling, and optional exogenous shocks, not solely through price as in classical Monte Carlo. We distinguish PTMC from adjacent paradigms, including classical Monte Carlo, hand-coded agent-based models, single-agent reinforcement learning, and large-language-model-based generative agents. To justify the design, we survey cross-disciplinary foundations -- agent-based computational economics, market microstructure, behavioral finance, deep reinforcement learning, generative/LLM-based agents, news-driven trading, systemic risk, econophysics, and game theory -- connecting each literature to a specific design choice in the policy network, training data, or validation protocol. We formalize the PTMC estimator and its convergence properties, specify a candidate bot architecture and training objective, and propose a four-level validation methodology: stylized-fact matching, microstructure- and agent-level checks, and historical stress-test comparison against a zero-intelligence baseline. The framework is proposed but not implemented: we contribute a formal estimator, a cross-disciplinary design justification, and a validation roadmap, and conclude with open research questions.

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Reliability and Identifiability in Persona-Trained Monte Carlo: Variance Decomposition, Stability Bounds, and the Identifiability of Heterogeneous News Reaction

Persona-Trained Monte Carlo (PTMC) estimates distributions of market-outcome functionals by repeatedly simulating limit-order-book interaction among KK neural policy bots whose behavioral personas are drawn from a learned heterogeneity distribution P\mathcal{P}. This paper develops the statistical theory that makes the word "reliable" precise for such estimators. We decompose estimator variance into a persona-draw component σP2σ_P^2 and a within-run component σw2σ_w^2, give unbiased ANOVA estimators of both, and derive the variance-optimal allocation of a fixed compute budget between outer persona draws and inner replications. A coupling-based stability bound quantifies how misestimation of P\mathcal{P} and error in the trained policy propagate into the estimand, yielding a three-term total-error budget whose terms are separately estimable; a uniform-in-horizon version holds under a Doeblin condition on the market chain. The main contribution is an identification theory for heterogeneous news reaction: under a fixed response nonlinearity, the aggregate impact curve A(z)=EQ[g(ηz)]A(z)=\mathbb{E}_Q[g(ηz)] detects heterogeneous news sensitivity through a strict Jensen gap and identifies the distribution QQ locally via odd moments and Hausdorff determinacy, with sharp failure when the response family is unknown. We provide n\sqrt{n}-consistent estimators and a boundary-corrected test of homogeneous news reaction. Two separation theorems delimit when PTMC is provably preferable to homogeneous-population simulators and reduced-form forecasters, formalizing an irreducible Jensen bias floor and the Lucas critique as a minimax limit on intervention extrapolation. All proofs are given in full; guarantees are classified as unconditional (Monte Carlo convergence), conditional worst-case (the error budget), or open (the large-KK mean-field limit).
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