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The Maximum-Entropy Distribution of the Future Market Price of a Stock

Author

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  • John M. Cozzolino

    (University of Pennsylvania, Philadelphia, Pennsylvania)

  • Michael J. Zahner

    (Sun Services Corporation, Philadelphia, Pennsylvania)

Abstract

This paper uses the principle of maximum entropy to construct a probability distribution of future stock price for a hypothetical investor having specified expectations. The result obtained is in good agreement with observations recorded in the literature. Thus, the paper concludes that the hypothetical individual investor is representative of a large class of investors. This new derivation of the well known random-walk theory of stock-price movements leads to an improved understanding of the model parameters by relating the variance of the random-walk process to the risk aversion of the investors. A practical use of the model is proposed to help the investor form an objective opinion of his skill.

Suggested Citation

  • John M. Cozzolino & Michael J. Zahner, 1973. "The Maximum-Entropy Distribution of the Future Market Price of a Stock," Operations Research, INFORMS, vol. 21(6), pages 1200-1211, December.
    • Handle: RePEc:inm:oropre:v:21:y:1973:i:6:p:1200-1211
    DOI: 10.1287/opre.21.6.1200
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    Cited by:

    1. David Nawrocki & Tonis Vaga, 2014. "A bifurcation model of market returns," Quantitative Finance, Taylor & Francis Journals, vol. 14(3), pages 509-528, March.
    2. Omid M. Ardakani, 2022. "Option pricing with maximum entropy densities: The inclusion of higher‐order moments," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(10), pages 1821-1836, October.
    3. Donald E. Brown & Robert L. Smith, 1990. "A correspondence principle for relative entropy minimization," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(2), pages 191-202, April.
    4. Moncer Hariga, 1998. "A single‐period, multi‐echelon stochastic model under a mix of assemble to order and assemble in advance policies," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(6), pages 599-614, September.
    5. Francisco Venegas & Enrique de Alba, 1995. "An Economist´s guide to the Kalman filter," Estudios Económicos, El Colegio de México, Centro de Estudios Económicos, vol. 10(2), pages 123-145.
    6. Alexis Toda, 2010. "Existence of a statistical equilibrium for an economy with endogenous offer sets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(3), pages 379-415, December.
    7. Malhotra, Gifty & Srivastava, R. & Taneja, H.C., 2019. "Calibration of the risk-neutral density function by maximization of a two-parameter entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 45-54.
    8. Nawrocki, David N., 1995. "Expectations, technological change, information and the theory of financial markets," International Review of Financial Analysis, Elsevier, vol. 4(2-3), pages 85-105.
    9. Gerardo Dubcovsky & Francisco Venegas-Martínez, 2003. "The Kalman Filter In The Event-Study Methodology," Remef - Revista Mexicana de Economía y Finanzas Nueva Época REMEF (The Mexican Journal of Economics and Finance), Instituto Mexicano de Ejecutivos de Finanzas, IMEF, vol. 2(1), pages 81-93, Marzo 200.
    10. Moon, Ilkyeong & Choi, Sangjin, 1997. "Distribution free procedures for make-to-order (MTO), make-in-advance (MIA), and composite policies," International Journal of Production Economics, Elsevier, vol. 48(1), pages 21-28, January.
    11. Lazov, Igor, 2017. "Profit management of car rental companies," European Journal of Operational Research, Elsevier, vol. 258(1), pages 307-314.
    12. Alwan, Layth C. & Ebrahimi, Nader & Soofi, Ehsan S., 1998. "Information theoretic framework for process control," European Journal of Operational Research, Elsevier, vol. 111(3), pages 526-542, December.
    13. Carrillo Murillo, David Guillermo & Liedtke, Gernot, 2013. "A model for the formation of colloidal structures in freight transportation: The case of hinterland terminals," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 49(1), pages 55-70.
    14. Colin Beardsley & John R. O'Brien, 2005. "The Financial Services Reform Act 2001: Impact on Systemic risk in Australia," ICMA Centre Discussion Papers in Finance icma-dp2005-12, Henley Business School, University of Reading.
    15. Smimou, K. & Bector, C.R. & Jacoby, G., 2007. "A subjective assessment of approximate probabilities with a portfolio application," Research in International Business and Finance, Elsevier, vol. 21(2), pages 134-160, June.
    16. Bogdan Grechuk & Anton Molyboha & Michael Zabarankin, 2009. "Maximum Entropy Principle with General Deviation Measures," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 445-467, May.

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