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Kyle-Back Models with risk aversion and non-Gaussian Beliefs

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  • Shreya Bose
  • Ibrahim Ekren

Abstract

We show that the problem of existence of equilibrium in Kyle's continuous time insider trading model can be tackled by considering a forward-backward system coupled via an optimal transport type constraint at maturity. The forward component is a stochastic differential equation representing an endogenously determined state variable and the backward component is a quasilinear parabolic equation representing the pricing function. By obtaining a stochastic representation for the solution of such a system, we show the well-posedness of solutions and study the properties of the equilibrium obtained for small enough risk aversion parameter. In our model, the insider has exponential type utility and the belief of the market maker on the distribution of the price at final time can be non-Gaussian.

Suggested Citation

  • Shreya Bose & Ibrahim Ekren, 2020. "Kyle-Back Models with risk aversion and non-Gaussian Beliefs," Papers 2008.06377, arXiv.org, revised Oct 2022.
    • Handle: RePEc:arx:papers:2008.06377
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    References listed on IDEAS

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    1. Kerry Back & Pierre Collin‐Dufresne & Vyacheslav Fos & Tao Li & Alexander Ljungqvist, 2018. "Activism, Strategic Trading, and Liquidity," Econometrica, Econometric Society, vol. 86(4), pages 1431-1463, July.
    2. Back, Kerry & Pedersen, Hal, 1998. "Long-lived information and intraday patterns," Journal of Financial Markets, Elsevier, vol. 1(3-4), pages 385-402, September.
    3. Guillaume Lasserre, 2004. "Asymmetric information and imperfect competition in a continuous time multivariate security model," Finance and Stochastics, Springer, vol. 8(2), pages 285-309, May.
    4. Luciano Campi & Umut Çetin, 2007. "Insider trading in an equilibrium model with default: a passage from reduced-form to structural modelling," Finance and Stochastics, Springer, vol. 11(4), pages 591-602, October.
    5. repec:dau:papers:123456789/4436 is not listed on IDEAS
    6. Back, Kerry, 1993. "Asymmetric Information and Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 435-472.
    7. Kerry Back & Francois Cocquemas & Ibrahim Ekren & Abraham Lioui, 2020. "Optimal Transport and Risk Aversion in Kyle's Model of Informed Trading," Papers 2006.09518, arXiv.org, revised Aug 2021.
    8. Campi, Luciano & Çetin, Umut & Danilova, Albina, 2011. "Dynamic Markov bridges motivated by models of insider trading," Stochastic Processes and their Applications, Elsevier, vol. 121(3), pages 534-567, March.
    9. Umut c{C}etin & Albina Danilova, 2014. "Markovian Nash equilibrium in financial markets with asymmetric information and related forward-backward systems," Papers 1407.2420, arXiv.org, revised Sep 2016.
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