A kinetic theory approach to consensus formation in financial markets

Jean-Gabriel Attali; Francesco Salvarani; Jean-Gabriel Attali; Francesco Salvarani

doi:10.3934/QFE.2026006

Quantitative Finance and Economics

2026, Volume 10, Issue 1: 108-129. doi: 10.3934/QFE.2026006

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Research article

A kinetic theory approach to consensus formation in financial markets

Jean-Gabriel Attali ¹,
Francesco Salvarani ^{1,2
,
,}

1.
De Vinci Higher Education, De Vinci Research Center, Paris, France
2.
Dipartimento di Matematica "F. Casorati", Università degli Studi di Pavia, Pavia, Italy

Received: 02 July 2025 Revised: 27 November 2025 Accepted: 12 January 2026 Published: 09 February 2026
JEL Codes: C63

It is sometimes acknowledged that (sell-side) equity analysts' recommendations influence investors and therefore market prices. In particular, the S&P 500 is expected to decline (or rise) when analysts revise their targets downward (upward, respectively). Our findings indicate not only that the analysts' consensus exert no influence on market prices, but also that, conversely, analysts appear to set their target prices based on markets prices. Employing a kinetic theory framework, we model the dynamics of the analysts' opinions, by taking both the mutual influences shaping price consensus and the dynamics of the actual S&P 500 index level into account. The model is calibrated on a training subset of data and tested on an independent set to assess its predictive power. Our tests show that just three free parameters are enough to accurately predict the one-year average price forecasts of analysts.
- S&P 500,
- cointegration,
- Kinetic modeling,
- forecast analysis
Citation: Jean-Gabriel Attali, Francesco Salvarani. A kinetic theory approach to consensus formation in financial markets[J]. Quantitative Finance and Economics, 2026, 10(1): 108-129. doi: 10.3934/QFE.2026006

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Abstract

It is sometimes acknowledged that (sell-side) equity analysts' recommendations influence investors and therefore market prices. In particular, the S&P 500 is expected to decline (or rise) when analysts revise their targets downward (upward, respectively). Our findings indicate not only that the analysts' consensus exert no influence on market prices, but also that, conversely, analysts appear to set their target prices based on markets prices. Employing a kinetic theory framework, we model the dynamics of the analysts' opinions, by taking both the mutual influences shaping price consensus and the dynamics of the actual S&P 500 index level into account. The model is calibrated on a training subset of data and tested on an independent set to assess its predictive power. Our tests show that just three free parameters are enough to accurately predict the one-year average price forecasts of analysts.

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