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Incomplete information equilibria: Separation theorems and other myths

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  • David Feldman

Abstract

The incomplete information financial economic equilibrium (IIE) literature has been growing at an increasing rate since its inception in the early 1980s. This paper examines issues and concepts essential to understanding, implementing, and testing IIE and understanding its relation to complete information equilibria (CIE). Concepts include the number of state variables in an IIE vis-à-vis the number of state variables in a corresponding CIE; the irrelevance of separation theorems to IIE and the relevance, instead, of a more general state space (re-)representation theorem; the identification of unobservable productivity processes that lead to complete information; the relative level of variable variances in a CIE and the corresponding IIE; stochastic CIE with corresponding deterministic IIE and deterministic CIE with corresponding stochastic IIE; the relationship between IIE and incomplete markets; the (im)persistence of heterogeneous beliefs; and the relation of IIE to the model uncertainty/ambiguity approaches. Understanding these concepts under IIE facilitates understanding the CIE, a special case of IIE. Copyright Springer Science+Business Media, LLC 2007

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  • David Feldman, 2007. "Incomplete information equilibria: Separation theorems and other myths," Annals of Operations Research, Springer, vol. 151(1), pages 119-149, April.
    • Handle: RePEc:spr:annopr:v:151:y:2007:i:1:p:119-149:10.1007/s10479-006-0119-3
    DOI: 10.1007/s10479-006-0119-3
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    1. Lundtofte, Frederik, 2008. "Expected life-time utility and hedging demands in a partially observable economy," European Economic Review, Elsevier, vol. 52(6), pages 1072-1096, August.
    2. Nikolai Dokuchaev, 2009. "Mutual Fund Theorem for continuous time markets with random coefficients," Papers 0911.3194, arXiv.org.
    3. Gau, Yin-Feng & Hua, Mingshu & Wu, Wen-Lin, 2010. "International asset allocation for incompletely-informed investors," Journal of Financial Markets, Elsevier, vol. 13(4), pages 422-447, November.
    4. Lubos Pastor & Pietro Veronesi, 2009. "Learning in Financial Markets," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 361-381, November.
    5. Nikolai Dokuchaev, 2015. "Optimal portfolio with unobservable market parameters and certainty equivalence principle," Papers 1502.02352, arXiv.org.
    6. Jacoby, Gady & Lee, Gemma & Paseka, Alexander & Wang, Yan, 2019. "Asset pricing with an imprecise information set," Pacific-Basin Finance Journal, Elsevier, vol. 53(C), pages 82-93.
    7. Wen-Lin Wu & Yin-Feng Gau, 2017. "Home bias in portfolio choices: social learning among partially informed agents," Review of Quantitative Finance and Accounting, Springer, vol. 48(2), pages 527-556, February.
    8. Tarik Driouchi & Lenos Trigeorgis & Raymond H. Y. So, 2018. "Option implied ambiguity and its information content: Evidence from the subprime crisis," Annals of Operations Research, Springer, vol. 262(2), pages 463-491, March.
    9. Frederik Lundtofte, 2009. "Can An 'Estimation Factor' Help Explain Cross-Sectional Returns?," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 36(5-6), pages 705-724.
    10. David Feldman & Xin Xu, 2018. "Equilibrium-based volatility models of the market portfolio rate of return (peacock tails or stotting gazelles)," Annals of Operations Research, Springer, vol. 262(2), pages 493-518, March.
    11. Frederik Lundtofte, 2013. "The quality of public information and the term structure of interest rates," Review of Quantitative Finance and Accounting, Springer, vol. 40(4), pages 715-740, May.
    12. Nikolai Dokuchaev, 2014. "Mutual Fund Theorem for continuous time markets with random coefficients," Theory and Decision, Springer, vol. 76(2), pages 179-199, February.
    13. Tomas Björk & Mark Davis & Camilla Landén, 2010. "Optimal investment under partial information," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(2), pages 371-399, April.
    14. Nikolai Dokuchaev, 2011. "The structure of optimal portfolio strategies for continuous time markets," Papers 1105.1488, arXiv.org, revised Apr 2014.
    15. Morita, Hiroshi & Okimoto, Tatsuyoshi, 2021. "The interest rate determination when economic variables are partially observable," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 72(C).
    16. Frederik Lundtofte, 2009. "Can An ‘Estimation Factor’ Help Explain Cross‐Sectional Returns?," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 36(5‐6), pages 705-724, June.

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