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Econophysics of Business Cycles: Aggregate Economic Fluctuations, Mean Risks and Mean Square Risks

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  • Victor Olkhov

Abstract

This paper presents hydrodynamic-like model of business cycles aggregate fluctuations of economic and financial variables. We model macroeconomics as ensemble of economic agents on economic space and agent's risk ratings play role of their coordinates. Sum of economic variables of agents with coordinate x define macroeconomic variables as functions of time and coordinates x. We describe evolution and interactions between macro variables on economic space by hydrodynamic-like equations. Integral of macro variables over economic space defines aggregate economic or financial variables as functions of time t only. Hydrodynamic-like equations define fluctuations of aggregate variables. Motion of agents from low risk to high risk area and back define the origin for repeated fluctuations of aggregate variables. Economic or financial variables on economic space may define statistical moments like mean risk, mean square risk and higher. Fluctuations of statistical moments describe phases of financial and economic cycles. As example we present a simple model relations between Assets and Revenue-on-Assets and derive hydrodynamic-like equations that describe evolution and interaction between these variables. Hydrodynamic-like equations permit derive systems of ordinary differential equations that describe fluctuations of aggregate Assets, Assets mean risks and Assets mean square risks. Our approach allows describe business cycle aggregate fluctuations induced by interactions between any number of economic or financial variables.

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  • Victor Olkhov, 2017. "Econophysics of Business Cycles: Aggregate Economic Fluctuations, Mean Risks and Mean Square Risks," Papers 1709.00282, arXiv.org.
    • Handle: RePEc:arx:papers:1709.00282
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    References listed on IDEAS

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    1. Sergio Rebelo, 2005. "Real Business Cycle Models: Past, Present and Future," Scandinavian Journal of Economics, Wiley Blackwell, vol. 107(2), pages 217-238, June.
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    5. Olkhov, Victor, 2016. "On Economic Space notion," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 372-381.
    6. Lucas, Robert E, Jr, 1980. "Methods and Problems in Business Cycle Theory," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 12(4), pages 696-715, November.
    7. Victor Olkhov, 2017. "Econophysics Macroeconomic Model," Papers 1701.06625, arXiv.org.
    8. Sergio Rebelo, 2005. "Real Business Cycle Models: Past, Present and Future," RCER Working Papers 522, University of Rochester - Center for Economic Research (RCER).
    9. repec:fip:fedreq:y:2011:i:3q:p:195-208:n:vol.97no.3 is not listed on IDEAS
    10. Victor Olkhov, 2017. "Non-Local Macroeconomic Transactions and Credits-Loans Surface-Like Waves," Papers 1706.07758, arXiv.org.
    11. Victor Olkhov, 2017. "Econophysics of Macroeconomics: "Action-at-a-Distance" and Waves," Papers 1702.02763, arXiv.org.
    12. Victor Olkhov, 2017. "Econophysics of Macro-Finance: Local Multi-fluid Models and Surface-like Waves of Financial Variables," Papers 1706.01748, arXiv.org.
    13. Victor Zarnowitz, 1992. "Business Cycles: Theory, History, Indicators, and Forecasting," NBER Books, National Bureau of Economic Research, Inc, number zarn92-1, July.
    14. Starr,Ross M., 2011. "General Equilibrium Theory," Cambridge Books, Cambridge University Press, number 9780521533867.
    15. Olkhov, Victor, 2017. "Quantitative wave model of macro-finance," International Review of Financial Analysis, Elsevier, vol. 50(C), pages 143-150.
    16. Olkhov, Victor, 2016. "Finance, risk and economic space," MPRA Paper 87172, University Library of Munich, Germany.
    17. Nobuhiro Kiyotaki, 2011. "A perspective on modern business cycle theory," Economic Quarterly, Federal Reserve Bank of Richmond, vol. 97(3Q), pages 195-208.
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    Cited by:

    1. Victor Olkhov, 2020. "Price, Volatility and the Second-Order Economic Theory," Papers 2009.14278, arXiv.org, revised Apr 2021.
    2. Olkhov, Victor, 2019. "New Essentials of Economic Theory I. Assumptions, Economic Space and Variables," MPRA Paper 93085, University Library of Munich, Germany.
    3. Olkhov, Victor, 2019. "New essentials of economic theory II. Economic transactions, expectations and asset pricing," MPRA Paper 93428, University Library of Munich, Germany.
    4. Victor Olkhov, 2022. "Why Economic Theories and Policies Fail? Unnoticed Variables and Overlooked Economics," Papers 2208.07839, arXiv.org.
    5. Victor Olkhov, 2018. "Econophysics Beyond General Equilibrium: the Business Cycle Model," Papers 1804.04721, arXiv.org.
    6. Victor Olkhov, 2019. "Econophysics of Asset Price, Return and Multiple Expectations," Papers 1901.05024, arXiv.org, revised Sep 2020.
    7. Olkhov, Victor, 2019. "Methods of Economic Theory: Variables, Transactions and Expectations as Functions of Risks," MPRA Paper 95628, University Library of Munich, Germany.
    8. Olkhov, Victor, 2023. "Economic complexity limits accuracy of price probability predictions by gaussian distributions," MPRA Paper 118373, University Library of Munich, Germany.
    9. Victor Olkhov, 2019. "Financial Variables, Market Transactions, and Expectations as Functions of Risk," IJFS, MDPI, vol. 7(4), pages 1-27, November.
    10. Victor Olkhov, 2020. "Business Cycles as Collective Risk Fluctuations," Papers 2012.04506, arXiv.org.
    11. Olkhov, Victor, 2019. "New Essentials of Economic Theory," MPRA Paper 95065, University Library of Munich, Germany.
    12. Olkhov, Victor, 2019. "New Essentials of Economic Theory III. Economic Applications," MPRA Paper 94053, University Library of Munich, Germany.

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