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

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.

We propose an index for predicting the U.S.\ Federal Open Market Committee (FOMC) decision to hike/hold/cut the current federal funds target rate based on how a collection of personas responds to current market conditions. To construct the index, we collected a new dataset consisting of nearly $25{,}000$ retrievable chunks from publicly available data. We partition the data into per-member corpora and use each as the retrieval database of a generative system we refer to throughout as a ``persona''. We first evaluate the personas across two complementary components of likeness: identifiability and detectability. Each persona's behavior is highly attributable (average member-conditional recall is $8\times$ chance) and generated content is nearly indistinguishable from held-out real content ($\hatτ_{\mathrm{det}} = 0.23$ against a $0.15$ floor). We then present evidence that query-conditioned representations of the personas capture members' monetary-policy stance relative to a known hawk--dove reputational ordering (Kendall's $τ= 0.63$, $p < 0.001$), substantially outperforming retrieval-only representations. These representations vary with time and current market conditions and form the basis of our proposed persona-based rate action index. For the $2022$--$2025$ period the index tracks the rate cycle (Kendall's $τ= 0.68$, $p < 10^{-6}$) and can be used to construct a simple classifier that predicts per-meeting outcomes at non-trivial accuracy ($0.69$ versus a $0.47$ base rate). Importantly, the index outperforms informative baselines and leads the federal funds target rate by roughly three quarters. As far as we are aware, our results are the first to demonstrate the ability to capture time-varying group behavior via a collection of digital personas.

The standard Monte Carlo estimator $\widehat{I}_N^{\mathrm{MC}}$ of $\int fdω$ relies on independent samples from $ω$ and has variance of order $1/N$. Replacing the samples with a determinantal point process (DPP), a repulsive distribution, makes the estimator consistent, with variance rates that depend on how the DPP is adapted to $f$ and $ω$. We examine two existing DPP-based estimators: one by Bardenet & Hardy (2020) with a rate of $\mathcal{O}(N^{-(1+1/d)})$ for smooth $f$, but relying on a fixed DPP. The other, by Ermakov & Zolotukhin (1960), is unbiased with rate of order $1/N$, like Monte Carlo, but its DPP is tailored to $f$. We revisit these estimators, generalize them to continuous settings, and provide sampling algorithms.