Reliability and Identifiability in Persona-Trained Monte Carlo: Variance Decomposition, Stability Bounds, and the Identifiability of Heterogeneous News Reaction
2026-07-06 • Machine Learning
Machine LearningComputational Engineering, Finance, and Science
AI summaryⓘ
The authors study a method called Persona-Trained Monte Carlo (PTMC), which simulates market interactions between different types of trading bots with varied behaviors to estimate market outcomes. They break down the estimator's variance into two parts and find the best way to balance computational effort between sampling different bot personas and repeated simulations. They also analyze how errors in learning bot behaviors affect the results and provide tests for detecting differences in how these bots react to news. Finally, the authors identify when their method outperforms simpler approaches, clarifying fundamental limits related to market models and policy changes.
Monte Carlo simulationlimit order bookheterogeneity distributionANOVAvariance decompositionDoeblin conditionJensen gapHausdorff determinacyLucas critiquemean-field limit
Authors
Salavat Ishbulatov
Abstract
Persona-Trained Monte Carlo (PTMC) estimates distributions of market-outcome functionals by repeatedly simulating limit-order-book interaction among $K$ neural policy bots whose behavioral personas are drawn from a learned heterogeneity distribution $\mathcal{P}$. This paper develops the statistical theory that makes the word "reliable" precise for such estimators. We decompose estimator variance into a persona-draw component $σ_P^2$ and a within-run component $σ_w^2$, 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 $\mathcal{P}$ 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 $A(z)=\mathbb{E}_Q[g(ηz)]$ detects heterogeneous news sensitivity through a strict Jensen gap and identifies the distribution $Q$ locally via odd moments and Hausdorff determinacy, with sharp failure when the response family is unknown. We provide $\sqrt{n}$-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-$K$ mean-field limit).