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On Equilibrium Existence in a Finite-Agent, Multi-Asset Noisy Rational Expectations Economy

Author

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  • Carpio Ronaldo

    (School of Banking and Finance, University of International Business and Economics, 913 Boxue Bldg, 10 Huixindongjie, Chaoyang District, Beijing, 100029, China)

  • Guo Meixin

    (School of Economics and Management, Tsinghua University, Beijing, 100084, China)

Abstract

We introduce a novel method of proving existence of rational expectations equilibria (REE) in multi-dimensional CARA-Gaussian environments. Our approach is to construct a mapping from agents’ initial beliefs (which are characterized by a positive semidefinite matrix), to their updated beliefs, after reaching and observing equilibrium; we then show Brouwer’s fixed point theorem applies. We apply our approach to a finite-market version of Admati (1985), which is a multi-asset noisy REE asset pricing model with dispersed information. We present an algorithm to numerically solve for equilibrium of the finite model, as well as several examples illustrating the difference in equilibrium behavior between the finite and infinite models. Our method can be applied to any multi-dimensional REE model with Gaussian uncertainty and behavior that is linear in agents’ information.

Suggested Citation

  • Carpio Ronaldo & Guo Meixin, 2020. "On Equilibrium Existence in a Finite-Agent, Multi-Asset Noisy Rational Expectations Economy," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 20(1), pages 1-17, January.
    • Handle: RePEc:bpj:bejtec:v:20:y:2020:i:1:p:17:n:4
    DOI: 10.1515/bejte-2018-0144
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    More about this item

    Keywords

    asymmetric information; noisy rational expectations; equilibrium existence;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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