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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.