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Differential Beliefs in Financial Markets Under Information Constraints: A Modeling Perspective

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  • Karen Grigorian
  • Robert Jarrow

Abstract

We apply the theory of McKean-Vlasov-type SDEs to study several problems related to market efficiency in the context of partial information and partially observable financial markets: (i) convergence of reduced-information market price processes to the true price process under an increasing information flow; (ii) a specific mechanism of shrinking biases under increasing information flows; (iii) optimal aggregation of expert opinions by a trader seeking a positive alpha. All these problems are studied by means of (conditional) McKean-Vlasov-type SDEs, Wasserstein barycenters, KL divergence and relevant tools from convex optimization, optimal control and nonlinear filtering. We supply the theoretical results in (i)-(iii) with concrete simulations demonstrating how the proposed models can be applied in practice to model financial markets under information constraints and the arbitrage-seeking behavior of traders with differential beliefs.

Suggested Citation

  • Karen Grigorian & Robert Jarrow, 2025. "Differential Beliefs in Financial Markets Under Information Constraints: A Modeling Perspective," Papers 2511.01486, arXiv.org, revised Nov 2025.
    • Handle: RePEc:arx:papers:2511.01486
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    References listed on IDEAS

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    1. Karen Grigorian & Robert A. Jarrow, 2023. "Enlargement of Filtrations: An Exposition of Core Ideas with Financial Examples," Papers 2303.03573, arXiv.org.
    2. Karen Grigorian & Robert A. jarrow, 2024. "Option Pricing in an Incomplete Market," Quarterly Journal of Finance (QJF), World Scientific Publishing Co. Pte. Ltd., vol. 14(03), pages 1-16, September.
    3. Karen Grigorian & Robert A. Jarrow, 2025. "No arbitrage for a special class of filtration expansions," Annals of Finance, Springer, vol. 21(1), pages 45-68, March.
    4. Xiong, Jie, 2008. "An Introduction to Stochastic Filtering Theory," OUP Catalogue, Oxford University Press, number 9780199219704.
    5. Sebastian Jaimungal & Silvana M. Pesenti, 2024. "Kullback-Leibler Barycentre of Stochastic Processes," Papers 2407.04860, arXiv.org, revised Apr 2025.
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