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Markovian Nash equilibrium in financial markets with asymmetric information and related forward-backward systems

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  • Çetin, Umut
  • Danilova, Albina

Abstract

This paper develops a new methodology for studying continuous-time Nash equilibrium in a financial market with asymmetrically informed agents. This approach allows us to lift the restriction of risk neutrality imposed on market makers by the current literature. It turns out that, when the market makers are risk averse, the optimal strategies of the agents are solutions of a forward- backward system of partial and stochastic differential equations. In particular, the price set by the market makers solves a non-standard `quadratic' backward stochastic differential equation. The main result of the paper is the existence of a Markovian solution to this forward-backward system on an arbitrary time interval, which is obtained via a fixed-point argument on the space of absolutely continuous distribution functions. Moreover, the equilibrium obtained in this paper is able to explain several stylized facts which are not captured by the current asymmetric information models.

Suggested Citation

  • Çetin, Umut & Danilova, Albina, 2016. "Markovian Nash equilibrium in financial markets with asymmetric information and related forward-backward systems," LSE Research Online Documents on Economics 63259, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:63259
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    File URL: http://eprints.lse.ac.uk/63259/
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Cetin, Umut, 2019. "Linear inverse problems for Markov processes and their regularisation," LSE Research Online Documents on Economics 102633, London School of Economics and Political Science, LSE Library.
    2. Jin Hyuk Choi & Heeyoung Kwon & Kasper Larsen, 2022. "Trading constraints in continuous-time Kyle models," Papers 2206.08117, arXiv.org.
    3. Reda Chhaibi & Ibrahim Ekren & Eunjung Noh & Lu Vy, 2022. "A unified approach to informed trading via Monge-Kantorovich duality," Papers 2210.17384, arXiv.org.
    4. L. C. Garcia Del Molino & I. Mastromatteo & Michael Benzaquen & J.-P. Bouchaud, 2019. "The Multivariate Kyle model: More is different," Working Papers hal-02323433, HAL.
    5. Ekström, Erik & Vaicenavicius, Juozas, 2020. "Optimal stopping of a Brownian bridge with an unknown pinning point," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 806-823.
    6. Ibrahim Ekren & Brad Mostowski & Gordan v{Z}itkovi'c, 2022. "Kyle's Model with Stochastic Liquidity," Papers 2204.11069, arXiv.org.
    7. Luis Carlos Garc'ia del Molino & Iacopo Mastromatteo & Michael Benzaquen & Jean-Philippe Bouchaud, 2018. "The Multivariate Kyle model: More is different," Papers 1806.07791, arXiv.org, revised Dec 2018.
    8. Mengütürk, Levent Ali, 2018. "Gaussian random bridges and a geometric model for information equilibrium," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 465-483.
    9. L. C. Garcia Del Molino & I. Mastromatteo & Michael Benzaquen & J.-P. Bouchaud, 2020. "The Multivariate Kyle model: More is different," Post-Print hal-02323433, HAL.
    10. Thibaut Mastrolia & Zhenjie Ren, 2017. "Principal-Agent Problem with Common Agency without Communication," Papers 1706.02936, arXiv.org, revised Jan 2018.
    11. Thibaut Mastrolia & Zhenjie Ren, 2018. "Principal-Agent Problem with Common Agency without Communication," Working Papers hal-01534611, HAL.
    12. Umut c{C}et{i}n, 2018. "Mathematics of Market Microstructure under Asymmetric Information," Papers 1809.03885, arXiv.org.
    13. Xing, Hao & Žitković, Gordan, 2018. "A class of globally solvable Markovian quadratic BSDE systems and applications," LSE Research Online Documents on Economics 73440, London School of Economics and Political Science, LSE Library.

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    More about this item

    Keywords

    Kyle model with risk averse market makers; Bertrand competition; forward–backward stochastic and partial differential equations; Markov bridges;
    All these keywords.

    JEL classification:

    • F3 - International Economics - - International Finance
    • G3 - Financial Economics - - Corporate Finance and Governance

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