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Dynamic Equilibrium with Insider Information and General Uninformed Agent Utility

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  • Jerome Detemple
  • Scott Robertson

Abstract

We study a continuous time economy where agents have asymmetric information. The informed agent (``$I$''), at time zero, receives a private signal about the risky assets' terminal payoff $\Psi(X_T)$, while the uninformed agent (``$U$'') has no private signal. $\Psi$ is an arbitrary payoff function, and $X$ follows a time-homogeneous diffusion. Crucially, we allow $U$ to have von Neumann-Morgenstern preferences with a general utility function on $(0,\infty)$ satisfying the standard conditions. This extends previous constructions of equilibria with asymmetric information used when all agents have exponential utilities and enables us to study the impact of $U$'s initial share endowment on equilibrium. To allow for $U$ to have general preferences, we introduce a new method to prove existence of a partial communication equilibrium (PCE), where at time $0$, $U$ receives a less-informative signal than $I$. In the single asset case, this signal is recoverable by viewing the equilibrium price process over an arbitrarily short period of time, and hence the PCE is a dynamic noisy rational expectations equilibrium. Lastly, when $U$ has power (constant relative risk aversion) utility, we identify the equilibrium price in the small and large risk aversion limits.

Suggested Citation

  • Jerome Detemple & Scott Robertson, 2022. "Dynamic Equilibrium with Insider Information and General Uninformed Agent Utility," Papers 2211.15573, arXiv.org, revised Mar 2024.
  • Handle: RePEc:arx:papers:2211.15573
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    References listed on IDEAS

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    1. Grossman, Sanford J, 1976. "On the Efficiency of Competitive Stock Markets Where Trades Have Diverse Information," Journal of Finance, American Finance Association, vol. 31(2), pages 573-585, May.
    2. Radner, Roy, 1979. "Rational Expectations Equilibrium: Generic Existence and the Information Revealed by Prices," Econometrica, Econometric Society, vol. 47(3), pages 655-678, May.
    3. Fontana, Claudio, 2018. "The strong predictable representation property in initially enlarged filtrations under the density hypothesis," Stochastic Processes and their Applications, Elsevier, vol. 128(3), pages 1007-1033.
    4. Amendinger, Jürgen & Imkeller, Peter & Schweizer, Martin, 1998. "Additional logarithmic utility of an insider," Stochastic Processes and their Applications, Elsevier, vol. 75(2), pages 263-286, July.
    5. Kramkov, Dmitry & Predoiu, Silviu, 2014. "Integral representation of martingales motivated by the problem of endogenous completeness in financial economics," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 81-100.
    6. Hellwig, Martin F., 1980. "On the aggregation of information in competitive markets," Journal of Economic Theory, Elsevier, vol. 22(3), pages 477-498, June.
    7. repec:dau:papers:123456789/13604 is not listed on IDEAS
    8. Amendinger, Jürgen, 2000. "Martingale representation theorems for initially enlarged filtrations," Stochastic Processes and their Applications, Elsevier, vol. 89(1), pages 101-116, September.
    9. J. Hugonnier & S. Malamud & E. Trubowitz, 2012. "Endogenous Completeness of Diffusion Driven Equilibrium Markets," Econometrica, Econometric Society, vol. 80(3), pages 1249-1270, May.
    10. Amendinger, Jürgen & Imkeller, Peter & Schweizer, Martin, 1998. "Additional logarithmic utility of an insider," SFB 373 Discussion Papers 1998,25, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    11. Jerome Detemple & Marcel Rindisbacher & Scott Robertson, 2020. "Dynamic Noisy Rational Expectations Equilibrium With Insider Information," Econometrica, Econometric Society, vol. 88(6), pages 2697-2737, November.
    12. Bradyn Breon-Drish, 2015. "On Existence and Uniqueness of Equilibrium in a Class of Noisy Rational Expectations Models," Review of Economic Studies, Oxford University Press, vol. 82(3), pages 868-921.
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    Cited by:

    1. Scott Robertson, 2023. "Equilibrium with Heterogeneous Information Flows," Papers 2304.01272, arXiv.org, revised Mar 2024.

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