IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v69y2009i3p379-394.html
   My bibliography  Save this article

Black swans and white eagles: on mathematics and finance

Author

Listed:
  • Sergio Focardi
  • Frank Fabozzi

Abstract

It is often objected that we cannot use mathematical methods in finance because (1) finance is dominated by unpredictable unique events (the black swans), (2) there are qualitative effects that cannot be quantified, and (3) the laws themselves of finance keep on changing. In this paper we discuss these three objections, offering arguments to reject them. We begin by reviewing the development of the physical sciences, pointing out parallels that are relevant for our discussion. Modern science has abandoned the objective of describing reality and has adopted an operational point of view that regards physical laws as tools to connect observations. Modern science is no longer deterministic, but has accepted a fundamental uncertainty in physical laws both at micro and macroscopic levels. Unpredictable pivotal events exist in the physical sciences as well in finance but this does not lead us to question the use of mathematics in the physical sciences. On the contrary, using principles of safe design, we try to understand how to avoid and contain unpredictability. Financial markets are manmade artifacts with, as actors, a large number of interacting agents. If we so wish, we can reduce the level of uncertainty present in markets: But if we try to do so describing financial markets with simple mathematical laws, we find that these laws are not stable but change over time, eventually with sudden structural breaks. This makes the use of mathematical finance difficult but not impossible. We can forecast human decision-making processes, crucial in forecasting financial markets, at the statistical level in aggregate. From an operational point of view, we have the tools to understand and describe the behavior of large number of interacting agents. At the present stage of development of our science, we need to use the mathematics of adaptive systems, changing mathematical models in function of different market states. However, reductionism to a small number of basic laws remains a fundamental objective of financial economics as it is in the physical sciences. Copyright Springer-Verlag 2009

Suggested Citation

  • Sergio Focardi & Frank Fabozzi, 2009. "Black swans and white eagles: on mathematics and finance," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(3), pages 379-394, July.
    • Handle: RePEc:spr:mathme:v:69:y:2009:i:3:p:379-394
    DOI: 10.1007/s00186-008-0243-8
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00186-008-0243-8
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00186-008-0243-8?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. Robert C. Merton, 2006. "Paul Samuelson and Financial Economics," The American Economist, Sage Publications, vol. 50(2), pages 9-31, October.
    2. Shiller, Robert J., 1999. "Human behavior and the efficiency of the financial system," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 20, pages 1305-1340, Elsevier.
    3. Edward L. Glaeser & Bruce Sacerdote & José A. Scheinkman, 1996. "Crime and Social Interactions," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 111(2), pages 507-548.
    4. Wesley Phoa & Sergio Focardi & Frank Fabozzi, 2007. "How do conflicting theories about financial markets coexist?," Journal of Post Keynesian Economics, Taylor & Francis Journals, vol. 29(3), pages 363-391.
    5. Lucas, Robert Jr, 1976. "Econometric policy evaluation: A critique," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 1(1), pages 19-46, January.
    6. Kydland, Finn E & Prescott, Edward C, 1977. "Rules Rather Than Discretion: The Inconsistency of Optimal Plans," Journal of Political Economy, University of Chicago Press, vol. 85(3), pages 473-491, 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. Kerem Uğurlu & Tomasz Brzeczek, 2023. "Distorted probability operator for dynamic portfolio optimization in times of socio-economic crisis," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 31(4), pages 1043-1060, December.

    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. Ftiti, Zied & Aguir, Abdelkader & Smida, Mounir, 2017. "Time-inconsistency and expansionary business cycle theories: What does matter for the central bank independence–inflation relationship?," Economic Modelling, Elsevier, vol. 67(C), pages 215-227.
    2. J. Subrick & Andrew Young, 2010. "Nobelity and novelty: Finn Kydland and Edward Prescott’s contributions viewed from Vienna," The Review of Austrian Economics, Springer;Society for the Development of Austrian Economics, vol. 23(1), pages 35-53, March.
    3. Aurélien Goutsmedt, 2021. "From the Stagflation to the Great Inflation: Explaining the US economy of the 1970s," Revue d'économie politique, Dalloz, vol. 131(3), pages 557-582.
    4. Berlemann, Michael & Hielscher, Kai, 2009. "Measuring Effective Monetary Policy Conservatism," Working Paper 89/2009, Helmut Schmidt University, Hamburg.
    5. Jordi Galí & Mark Gertler, 2007. "Macroeconomic Modeling for Monetary Policy Evaluation," Journal of Economic Perspectives, American Economic Association, vol. 21(4), pages 25-46, Fall.
    6. Goodhart, Charles, 1989. "The Conduct of Monetary Policy," Economic Journal, Royal Economic Society, vol. 99(396), pages 293-346, June.
    7. Andrea Bonilla‐Bolaños, 2021. "A step further in the theory of regional integration: A look at the South American integration strategy," Journal of International Development, John Wiley & Sons, Ltd., vol. 33(5), pages 845-873, July.
    8. Gissler, Stefan & Oldfather, Jeremy & Ruffino, Doriana, 2016. "Lending on hold: Regulatory uncertainty and bank lending standards," Journal of Monetary Economics, Elsevier, vol. 81(C), pages 89-101.
    9. Lucas Papademos, 2005. "Macroeconomic theory and monetary policy: the contributions of Franco Modigliani and the ongoing debate," BNL Quarterly Review, Banca Nazionale del Lavoro, vol. 58(233-234), pages 187-214.
    10. Aurélien Goutsmedt, 2016. "The New Classical Explanation of the Stagflation: A Psychological Way of Thinking," Documents de travail du Centre d'Economie de la Sorbonne 16018, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    11. Masciandaro, Donato, 2022. "Independence, conservatism, and beyond: Monetary policy, central bank governance and central banker preferences (1981–2021)," Journal of International Money and Finance, Elsevier, vol. 122(C).
    12. Joshua D. Angrist & Jörn-Steffen Pischke, 2010. "The Credibility Revolution in Empirical Economics: How Better Research Design Is Taking the Con out of Econometrics," Journal of Economic Perspectives, American Economic Association, vol. 24(2), pages 3-30, Spring.
    13. Stephen J. Turnovsky, 2011. "Stabilization Theory and Policy: 50 Years after the Phillips Curve," Economica, London School of Economics and Political Science, vol. 78(309), pages 67-88, January.
    14. Monique Reid & Pierre Siklos, 2023. "Rationality and biases insights from disaggregated firm level inflation expectations data," Working Papers 11050, South African Reserve Bank.
    15. Michael Woodford, 1999. "Optimal Monetary Policy Inertia," Manchester School, University of Manchester, vol. 67(s1), pages 1-35.
    16. Eaton, Jonathan, 1985. "Optimal and time consistent exchange-rate management in an overlapping-generations economy," Journal of International Money and Finance, Elsevier, vol. 4(1), pages 83-100, March.
    17. Athreya, Kartik B., 2014. "Big Ideas in Macroeconomics: A Nontechnical View," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262019736, December.
    18. Michelle Baddeley, 2019. "Behavioural Macroeconomic Policy: New perspectives on time inconsistency," Papers 1907.07858, arXiv.org.
    19. Gáti, Laura, 2023. "Monetary policy & anchored expectations—An endogenous gain learning model," Journal of Monetary Economics, Elsevier, vol. 140(S), pages 37-47.
    20. Alan S. Blinder, 2019. "What does Jerome Powell know that William McChesney Martin didn’t—and what role did academic research play in that?," Working Papers 259, Princeton University, Department of Economics, Center for Economic Policy Studies..

    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:mathme:v:69:y:2009:i:3:p:379-394. 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.