IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v151y2007i1p119-14910.1007-s10479-006-0119-3.html
   My bibliography  Save this article

Incomplete information equilibria: Separation theorems and other myths

Author

Listed:
  • 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

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-006-0119-3
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-006-0119-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Hansen, Lars Peter & Sargent, Thomas J., 1982. "Instrumental variables procedures for estimating linear rational expectations models," Journal of Monetary Economics, Elsevier, vol. 9(3), pages 263-296.
    2. Michael W. Brandt & Amit Goyal & Pedro Santa-Clara & Jonathan R. Stroud, 2005. "A Simulation Approach to Dynamic Portfolio Choice with an Application to Learning About Return Predictability," The Review of Financial Studies, Society for Financial Studies, vol. 18(3), pages 831-873.
    3. Lakner, Peter, 1998. "Optimal trading strategy for an investor: the case of partial information," Stochastic Processes and their Applications, Elsevier, vol. 76(1), pages 77-97, August.
    4. Frank Riedel, 2004. "Heterogeneous time preferences and interest rates—the preferred habitat theory revisited," The European Journal of Finance, Taylor & Francis Journals, vol. 10(1), pages 3-22.
    5. Gennotte, Gerard, 1986. "Optimal Portfolio Choice under Incomplete Information," Journal of Finance, American Finance Association, vol. 41(3), pages 733-746, July.
    6. 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.
    7. Peng, Lin, 2005. "Learning with Information Capacity Constraints," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 40(2), pages 307-329, June.
    8. Kandel, Shmuel & Stambaugh, Robert F, 1996. "On the Predictability of Stock Returns: An Asset-Allocation Perspective," Journal of Finance, American Finance Association, vol. 51(2), pages 385-424, June.
    9. 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.
    10. Jakša Cvitanić & Ali Lazrak & Lionel Martellini & Fernando Zapatero, 2006. "Dynamic Portfolio Choice with Parameter Uncertainty and the Economic Value of Analysts' Recommendations," The Review of Financial Studies, Society for Financial Studies, vol. 19(4), pages 1113-1156.
    11. N. Dokuchaev & U. Haussmann, 2001. "Optimal portfolio selection and compression in an incomplete market," Quantitative Finance, Taylor & Francis Journals, vol. 1(3), pages 336-345, March.
    12. Frank Riedel, 2000. "Decreasing Yield Curves in a Model with an Unknown Constant Growth Rate," Review of Finance, European Finance Association, vol. 4(1), pages 51-67.
    13. Jiang Wang, 1993. "A Model of Intertemporal Asset Prices Under Asymmetric Information," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(2), pages 249-282.
    14. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    15. Hakansson, Nils H, 1971. "On Optimal Myopic Portfolio Policies, With and Without Serial Correlation of Yields," The Journal of Business, University of Chicago Press, vol. 44(3), pages 324-334, July.
    16. Paul Childs & Steven Ott & Timothy Riddiough, 2001. "Valuation and Information Acquisition Policy for Claims Written on Noisy Real Assets," Financial Management, Financial Management Association, vol. 30(2), Summer.
    17. David Feldman, 2003. "The Term Structure of Interest Rates: Bounded or Falling?," Review of Finance, European Finance Association, vol. 7(1), pages 103-113.
    18. David Feldman, 1989. "The Term Structure of Interest Rates in a Partially Observable Economy," Journal of Finance, American Finance Association, vol. 44(3), pages 789-812, July.
    19. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    20. Massimo Massa, 2002. "Financial Innovation and Information: The Role of Derivatives When a Market for Information Exists," The Review of Financial Studies, Society for Financial Studies, vol. 15(3), pages 927-957.
    21. Paul A. Samuelson, 2011. "Lifetime Portfolio Selection by Dynamic Stochastic Programming," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 31, pages 465-472, World Scientific Publishing Co. Pte. Ltd..
    22. Jeffrey, Andrew, 1995. "Single Factor Heath-Jarrow-Morton Term Structure Models Based on Markov Spot Interest Rate Dynamics," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 30(4), pages 619-642, December.
    23. Jonathan Lewellen & Jay Shanken, 2002. "Learning, Asset‐Pricing Tests, and Market Efficiency," Journal of Finance, American Finance Association, vol. 57(3), pages 1113-1145, June.
    24. Alexandre Ziegler, 2000. "Optimal Portfolio Choice under Heterogeneous Beliefs," Review of Finance, European Finance Association, vol. 4(1), pages 1-19.
    25. Dokuchaev, Nikolai G. & Savkin, Andrey V., 2002. "A bounded risk strategy for a market with non-observable parameters," Insurance: Mathematics and Economics, Elsevier, vol. 30(2), pages 243-254, April.
    26. David, Alexander, 1997. "Fluctuating Confidence in Stock Markets: Implications for Returns and Volatility," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 32(4), pages 427-462, December.
    27. Riedel, Frank, 2001. "Existence of Arrow-Radner Equilibrium with Endogenously Complete Markets under Incomplete Information," Journal of Economic Theory, Elsevier, vol. 97(1), pages 109-122, March.
    28. Li, George, 2005. "Information Quality, Learning, and Stock Market Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 40(3), pages 595-620, September.
    29. Williams, Joseph T., 1977. "Capital asset prices with heterogeneous beliefs," Journal of Financial Economics, Elsevier, vol. 5(2), pages 219-239, November.
    30. Andrew Mark Jeffrey, 1995. "Single Factor Heath-Jarrow-Morton Term Structure Models Based on Markov Spot Interest Rate Dynamics," Yale School of Management Working Papers ysm46, Yale School of Management.
    31. Merton, Robert C., 1980. "On estimating the expected return on the market : An exploratory investigation," Journal of Financial Economics, Elsevier, vol. 8(4), pages 323-361, December.
    32. Ľuboš Pástor, 2000. "Portfolio Selection and Asset Pricing Models," Journal of Finance, American Finance Association, vol. 55(1), pages 179-223, February.
    33. Wang, Neng, 2004. "Precautionary saving and partially observed income," Journal of Monetary Economics, Elsevier, vol. 51(8), pages 1645-1681, November.
    34. Dothan, Michael U & Feldman, David, 1986. "Equilibrium Interest Rates and Multiperiod Bonds in a Partially Observable Economy," Journal of Finance, American Finance Association, vol. 41(2), pages 369-382, June.
    35. Honda, Toshiki, 2003. "Optimal portfolio choice for unobservable and regime-switching mean returns," Journal of Economic Dynamics and Control, Elsevier, vol. 28(1), pages 45-78, October.
    36. Ketterer, Joan A., 1990. "Approximation theorems for stochastic economies with incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 269-284.
    37. L.C.G. Rogers, 2001. "The relaxed investor and parameter uncertainty," Finance and Stochastics, Springer, vol. 5(2), pages 131-154.
    38. Yoichi Kuwana, 1995. "Certainty Equivalence And Logarithmic Utilities In Consumption/Investment Problems," Mathematical Finance, Wiley Blackwell, vol. 5(4), pages 297-309, October.
    39. Lundtofte, Frederik, 2005. "Can An ”Estimation Factor” Help Explain Cross-Sectional Returns?," Working Papers 2005:18, Lund University, Department of Economics.
    40. Yihong Xia, 2001. "Learning about Predictability: The Effects of Parameter Uncertainty on Dynamic Asset Allocation," Journal of Finance, American Finance Association, vol. 56(1), pages 205-246, February.
    41. Basak, Suleyman, 2000. "A model of dynamic equilibrium asset pricing with heterogeneous beliefs and extraneous risk," Journal of Economic Dynamics and Control, Elsevier, vol. 24(1), pages 63-95, January.
    42. M. J. Brennan, 1998. "The Role of Learning in Dynamic Portfolio Decisions," Review of Finance, European Finance Association, vol. 1(3), pages 295-306.
    43. Coles, Jeffrey L. & Loewenstein, Uri, 1988. "Equilibrium pricing and portfolio composition in the presence of uncertain parameters," Journal of Financial Economics, Elsevier, vol. 22(2), pages 279-303, December.
    44. Massa, Massimo & Simonov, Andrei, 2005. "Is learning a dimension of risk?," Journal of Banking & Finance, Elsevier, vol. 29(10), pages 2605-2632, October.
    45. Jörn Sass & Ulrich Haussmann, 2004. "Optimizing the terminal wealth under partial information: The drift process as a continuous time Markov chain," Finance and Stochastics, Springer, vol. 8(4), pages 553-577, November.
    46. Hart, Oliver D., 1974. "On the existence of equilibrium in a securities model," Journal of Economic Theory, Elsevier, vol. 9(3), pages 293-311, November.
    47. Timothy C. Johnson, 2001. "Return Dynamics when Persistence is Unobservable," Mathematical Finance, Wiley Blackwell, vol. 11(4), pages 415-445, October.
    48. Bates, David S., 2003. "Empirical option pricing: a retrospection," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 387-404.
    49. Pietro Veronesi, 2000. "How Does Information Quality Affect Stock Returns?," Journal of Finance, American Finance Association, vol. 55(2), pages 807-837, April.
    50. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    51. Ziegler, Alexandre, 2002. "State-price densities under heterogeneous beliefs, the smile effect, and implied risk aversion," European Economic Review, Elsevier, vol. 46(8), pages 1539-1557, September.
    52. Abraham Lioui & Patrice Poncet, 2000. "Bernoulli speculator and trading strategy risk," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 20(6), pages 507-523, July.
    53. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    54. Detemple, Jerome B., 1991. "Further results on asset pricing with incomplete information," Journal of Economic Dynamics and Control, Elsevier, vol. 15(3), pages 425-453, July.
    55. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    56. Feldman, David, 1992. "Logarithmic Preferences, Myopic Decisions, and Incomplete Information," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 27(4), pages 619-629, December.
    57. Wang, Jiang, 1994. "A Model of Competitive Stock Trading Volume," Journal of Political Economy, University of Chicago Press, vol. 102(1), pages 127-168, February.
    58. MOSSIN, Jan, 1968. "Optimal multiperiod portfolio policies," LIDAM Reprints CORE 19, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    59. Naik, Narayan Y., 1997. "On aggregation of information in competitive markets: The dynamic case," Journal of Economic Dynamics and Control, Elsevier, vol. 21(7), pages 1199-1227, June.
    60. Johnson, Timothy C, 2002. "Volatility, Momentum, and Time-Varying Skewness in Foreign Exchange Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 390-411, July.
    61. Detemple, Jerome B., 2002. "Asset pricing in an intertemporal partially-revealing rational expectations equilibrium," Journal of Mathematical Economics, Elsevier, vol. 38(1-2), pages 219-248, September.
    62. Kuwana, Yoichi, 1999. "A Minimax Analysis of Merton's Problem," Hitotsubashi Journal of Economics, Hitotsubashi University, vol. 40(2), pages 123-128, December.
    63. David Feldman, 2002. "Production and the Real Rate of Interest: A Sample Path Equilibrium," Review of Finance, European Finance Association, vol. 6(2), pages 247-275.
    64. Zapatero, Fernando, 1998. "Effects of financial innovations on market volatility when beliefs are heterogeneous," Journal of Economic Dynamics and Control, Elsevier, vol. 22(4), pages 597-626, April.
    65. Detemple, Jerome B, 1986. "Asset Pricing in a Production Economy with Incomplete Information," Journal of Finance, American Finance Association, vol. 41(2), pages 383-391, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Nikolai Dokuchaev, 2011. "The structure of optimal portfolio strategies for continuous time markets," Papers 1105.1488, arXiv.org, revised Apr 2014.
    7. 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.
    8. Nikolai Dokuchaev, 2009. "Mutual Fund Theorem for continuous time markets with random coefficients," Papers 0911.3194, arXiv.org.
    9. Lubos Pastor & Pietro Veronesi, 2009. "Learning in Financial Markets," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 361-381, November.
    10. Nikolai Dokuchaev, 2015. "Optimal portfolio with unobservable market parameters and certainty equivalence principle," Papers 1502.02352, arXiv.org.
    11. 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.
    12. 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.
    13. 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.
    14. Nikolai Dokuchaev, 2014. "Mutual Fund Theorem for continuous time markets with random coefficients," Theory and Decision, Springer, vol. 76(2), pages 179-199, February.
    15. 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.
    16. 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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lubos Pastor & Pietro Veronesi, 2009. "Learning in Financial Markets," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 361-381, November.
    2. 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.
    3. 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.
    4. 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.
    5. Constantin Mellios, 2007. "Interest rate options valuation under incomplete information," Annals of Operations Research, Springer, vol. 151(1), pages 99-117, April.
    6. Daniel Andrei & Michael Hasler, 2020. "Dynamic Attention Behavior Under Return Predictability," Management Science, INFORMS, vol. 66(7), pages 2906-2928, July.
    7. Michele Longo & Alessandra Mainini, 2016. "Learning And Portfolio Decisions For Crra Investors," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-21, May.
    8. Michele Longo & Alessandra Mainini, 2015. "Learning and Portfolio Decisions for HARA Investors," Papers 1502.02968, arXiv.org.
    9. Basak, Suleyman, 2005. "Asset pricing with heterogeneous beliefs," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2849-2881, November.
    10. Penaranda, Francisco, 2007. "Portfolio choice beyond the traditional approach," LSE Research Online Documents on Economics 24481, London School of Economics and Political Science, LSE Library.
    11. John Y. Campbell, 2000. "Asset Pricing at the Millennium," Journal of Finance, American Finance Association, vol. 55(4), pages 1515-1567, August.
    12. Liu, Hening, 2011. "Dynamic portfolio choice under ambiguity and regime switching mean returns," Journal of Economic Dynamics and Control, Elsevier, vol. 35(4), pages 623-640, April.
    13. Hui Chen & Nengjiu Ju & Jianjun Miao, 2014. "Dynamic Asset Allocation with Ambiguous Return Predictability," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 17(4), pages 799-823, October.
    14. Jonathan Lewellen & Jay Shanken, 2002. "Learning, Asset‐Pricing Tests, and Market Efficiency," Journal of Finance, American Finance Association, vol. 57(3), pages 1113-1145, June.
    15. 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.
    16. Basak, Suleyman, 2004. "Asset Prices with Heterogenous Beliefs," CEPR Discussion Papers 4256, C.E.P.R. Discussion Papers.
    17. Hening Liu, 2011. "Dynamic portfolio choice under ambiguity and regime switching mean returns," Post-Print hal-00781344, HAL.
    18. Daniel Andrei & Bruce Carlin & Michael Hasler, 2019. "Asset Pricing with Disagreement and Uncertainty About the Length of Business Cycles," Management Science, INFORMS, vol. 67(6), pages 2900-2923, June.
    19. 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.
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:151:y:2007:i:1:p:119-149:10.1007/s10479-006-0119-3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.