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On Economic Space notion

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  • Olkhov, Victor

Abstract

This paper introduces Economic Space notion to expand capacity for economic and financial modeling. Introduction of Economic Space allows defining economic variables as functions of time and coordinates and opens the way for treating economic and financial relations similar to mathematical physics equations. Economic Space allows study of economic models on discreet and continuous spaces with different dimensions. The number of risks measured simultaneously determines Economic Space dimension. We present examples of modeling on Economic Space: option pricing and derivation of Black–Scholes–Merton equation on n-dimensional Economic Space; Markov processes and derivation of Fokker–Plank Equations. Usage of Economic Space allows construing approximations of Economics and Finance similar to physical kinetics and hydrodynamics and derives Wave Equations for Economic and Financial variables.

Suggested Citation

  • Olkhov, Victor, 2016. "On Economic Space notion," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 372-381.
    • Handle: RePEc:eee:finana:v:47:y:2016:i:c:p:372-381
    DOI: 10.1016/j.irfa.2016.01.001
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    References listed on IDEAS

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    1. Merton, Robert C, 1998. "Applications of Option-Pricing Theory: Twenty-Five Years Later," American Economic Review, American Economic Association, vol. 88(3), pages 323-349, June.
    2. Klaus Reiner Schenk-Hopp�, "undated". "Random Dynamical Systems in Economics," IEW - Working Papers 067, Institute for Empirical Research in Economics - University of Zurich.
    3. McCauley, Joseph L., 2006. "Response to worrying trends in econophysics," MPRA Paper 2129, University Library of Munich, Germany.
    4. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    5. Roehner,Bertrand M., 2002. "Patterns of Speculation," Cambridge Books, Cambridge University Press, number 9780521802635, October.
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    8. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    9. repec:asg:wpaper:1013 is not listed on IDEAS
    10. Francis X. Diebold, 1998. "The Past, Present, and Future of Macroeconomic Forecasting," Journal of Economic Perspectives, American Economic Association, vol. 12(2), pages 175-192, Spring.
    11. McCauley,Joseph L., 2013. "Stochastic Calculus and Differential Equations for Physics and Finance," Cambridge Books, Cambridge University Press, number 9780521763400, October.
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    Citations

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    Cited by:

    1. Olkhov, Victor, 2016. "On Hidden Problems of Option Pricing," MPRA Paper 87173, University Library of Munich, Germany.
    2. Olkhov, Victor, 2018. "Expectations, Price Fluctuations and Lorenz Attractor," MPRA Paper 89105, University Library of Munich, Germany.
    3. Olkhov, Victor, 2018. "The Business Cycle Model Beyond General Equilibrium," MPRA Paper 87204, University Library of Munich, Germany.
    4. Olkhov, Victor, 2017. "Quantitative wave model of macro-finance," International Review of Financial Analysis, Elsevier, vol. 50(C), pages 143-150.
    5. Victor Olkhov, 2017. "Econophysics Macroeconomic Model," Papers 1701.06625, arXiv.org.
    6. Olkhov, Victor, 2020. "Price, Volatility and the Second-Order Economic Theory," MPRA Paper 102767, University Library of Munich, Germany.
    7. Olkhov, Victor, 2018. "Economic and Financial Transactions Govern Business Cycles," MPRA Paper 93269, University Library of Munich, Germany.
    8. Victor Olkhov, 2018. "Econophysics Beyond General Equilibrium: the Business Cycle Model," Papers 1804.04721, arXiv.org.
    9. Victor Olkhov, 2017. "Econophysics of Business Cycles: Aggregate Economic Fluctuations, Mean Risks and Mean Square Risks," Papers 1709.00282, arXiv.org.
    10. Olkhov, Victor, 2020. "Classical Option Pricing and Some Steps Further," MPRA Paper 105431, University Library of Munich, Germany, revised 28 Dec 2020.
    11. Victor Olkhov, 2020. "Business Cycles as Collective Risk Fluctuations," Papers 2012.04506, arXiv.org.
    12. Olkhov, Victor, 2018. "Economic Transactions Govern Business Cycles," MPRA Paper 87207, University Library of Munich, Germany.
    13. Victor Olkhov, 2017. "Econophysics of Macro-Finance: Local Multi-fluid Models and Surface-like Waves of Financial Variables," Papers 1706.01748, arXiv.org.
    14. Victor Olkhov, 2019. "Econophysics of Asset Price, Return and Multiple Expectations," Papers 1901.05024, arXiv.org, revised Sep 2020.
    15. Victor Olkhov, 2018. "How Macro Transactions Describe the Evolution and Fluctuation of Financial Variables," IJFS, MDPI, vol. 6(2), pages 1-19, March.
    16. Olkhov, Victor, 2017. "Quantitative Description of Financial Transactions and Risks," MPRA Paper 87316, University Library of Munich, Germany.
    17. Victor Olkhov, 2019. "Financial Variables, Market Transactions, and Expectations as Functions of Risk," IJFS, MDPI, vol. 7(4), pages 1-27, November.
    18. Victor Olkhov, 2021. "Theoretical Economics and the Second-Order Economic Theory. What is it?," Papers 2112.04566, arXiv.org, revised Mar 2024.
    19. Victor Olkhov, 2017. "Non-Local Macroeconomic Transactions and Credits-Loans Surface-Like Waves," Papers 1706.07758, arXiv.org.
    20. Baker, H. Kent & Kumar, Satish & Goyal, Kirti & Sharma, Anuj, 2021. "International review of financial analysis: A retrospective evaluation between 1992 and 2020," International Review of Financial Analysis, Elsevier, vol. 78(C).

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    More about this item

    Keywords

    Financial modeling; Economic space; Risk ratings; Economic wave equations;
    All these keywords.

    JEL classification:

    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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