Original title: Mean-field equilibrium of heterogeneous agents under market impact
Joseph Leclère, Mathieu Rosenbaum · September 2026
Traders often share the same news, but they plan over different time horizons. When they buy or sell, their shared trading moves asset prices, altering the very market they tried to forecast. The researchers built a mathematical model to study this loop. In their model, the market price has three parts: a random component, a shared predictable signal, and the price change caused by all traders combined. Each trader bets on where the signal is heading while trying to anticipate this shared price impact. The authors proved that a single, stable balance point exists. At this balance, the shared signal and the trading impact can cancel each other out. If traders fully account for their market impactHow buying or selling in volume changes the market price., the predictable signal disappears, and the price behaves purely like an unpredictable random walk. The team also determined which mix of horizons produces standard price patterns.
Imagine you are deciding what to wear based on a weather forecast, but your outfit choice affects the weather for everyone else. If you pick a coat, it somehow makes it rain for others, changing their forecasts. In this paper, traders decide trades based on forecasts, but their trades change prices, which alters the forecasts. When everyone considers this feedback, the price ends up unpredictable.
Market prices affect investments, pensions, and economic decisions for millions. If traders with different time horizons distort prices through collective actions, it can lead to mispricing or instability. This model reveals how such behavior might stabilize prices into randomness under certain conditions.
The abstract does not mention empirical testing with real market data. The model relies on specific mathematical assumptions, such as a Gaussian-Volterra framework and fractional-type signals, which may not cover all market scenarios.
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Mean-field equilibrium of heterogeneous agents under market impact — Joseph Leclère, Mathieu Rosenbaum
Abstract licence: CC0
Explanation generated by Synthesis from the abstract — it is not the original paper. This is a preprint, so it hasn't necessarily been peer reviewed.