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Liquidity generated by heterogeneous beliefs and costly estimations

Author

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  • Min Shen

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

  • Gabriel Turinici

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

Abstract

We study the liquidity, de ned as the size of the trading volume, in a situation where an in nite number of agents with heterogeneous beliefs reach a trade-o between the cost of a precise estimation (variable depending on the agent) and the expected wealth from trading. The \true" asset price is not known and the market price is set at a level that clears the market. We show that, under some technical assumptions, the model has natural properties such as monotony of supply and demand functions with respect to the price, existence of an equilibrium and monotony with respect to the marginal cost of information. We also situate our approach within the Mean Field Games (MFG) framework of Lions and Lasry which allows to obtain an interpretation as a limit of Nash equilibrium for an in nite number of agents.

Suggested Citation

  • Min Shen & Gabriel Turinici, 2012. "Liquidity generated by heterogeneous beliefs and costly estimations," Post-Print hal-00638966, HAL.
    • Handle: RePEc:hal:journl:hal-00638966
    DOI: 10.3934/nhm.2012.7.349
    Note: View the original document on HAL open archive server: https://hal.science/hal-00638966v5
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    References listed on IDEAS

    as
    1. Jouini, Elyes & Napp, Clotilde, 2006. "Heterogeneous beliefs and asset pricing in discrete time: An analysis of pessimism and doubt," Journal of Economic Dynamics and Control, Elsevier, vol. 30(7), pages 1233-1260, July.
    2. Jouini, E. & Napp, C., 2006. "Aggregation of heterogeneous beliefs," Journal of Mathematical Economics, Elsevier, vol. 42(6), pages 752-770, September.
    3. Marco Avellaneda & Sasha Stoikov, 2008. "High-frequency trading in a limit order book," Quantitative Finance, Taylor & Francis Journals, vol. 8(3), pages 217-224.
    4. repec:dau:papers:123456789/341 is not listed on IDEAS
    5. repec:dau:papers:123456789/80 is not listed on IDEAS
    6. Michael Gallmeyer & Burton Hollifield, 2008. "An Examination of Heterogeneous Beliefs with a Short-Sale Constraint in a Dynamic Economy," Review of Finance, European Finance Association, vol. 12(2), pages 323-364.
    7. repec:hal:journl:halshs-00176505 is not listed on IDEAS
    8. Clotilde Napp & Elyès Jouini, 2006. "Heterogeneous Beliefs and Asset Pricing in Discrete Time," Post-Print halshs-00151536, HAL.
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    Cited by:

    1. Mathieu Laurière & Olivier Pironneau, 2016. "Dynamic Programming for Mean-Field Type Control," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 902-924, June.
    2. Agnes Bialecki & Eleonore Haguet & Gabriel Turinici, 2014. "Existence of an Equilibrium for Lower Semicontinuous Information Acquisition Functions," Post-Print hal-00723189, HAL.

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