Advertisement

Is Risk Quantifiable?

  • Sami Al-SuwailemEmail author
  • Francisco A. Doria
  • Mahmoud Kamel
Conference paper
Part of the Springer Proceedings in Complexity book series (SPCOM)

Abstract

The work of Gödel and Turing, among others, shows that there are fundamental limits to the possibility of formal quantification of natural and social phenomena . Both our knowledge and our ignorance are, to a large extent, not amenable to quantification. Disregard of these limits in the economic sphere might lead to underestimation of risk and, consequently, to excessive risk-taking. If so, this would expose markets to undue instability and turbulence. One major lesson of the Global Financial Crisis, therefore, is to reform economic methodology to expand beyond formal reasoning.

Keywords

Financial instability Gödel’s incompleteness theorem Irreducible uncertainty Lucas critique Mispricing risk Quantifiability of risk Reflexivity Rice’s theorem Self-reference 

Notes

Acknowledgements

We are grateful to the editors and an anonymous referee for constructive comments and suggestions that greatly improved the readability of this text. FAD: wishes to acknowledge research grant no. 4339819902073398 from CNPq/Brazil, and the support of the Production Engineering Program, coppe/UFRJ, Brazil. SA: wishes to acknowledge the valuable discussions with the co-authors, particularly FAD. The views expressed in this chapter do not necessarily represent the views of the Islamic Development Bank Group.

References

  1. 1.
    Al-Suwailem, S. (2010). Behavioural complexity. Journal of Economic Surveys, 25, 481–506.CrossRefGoogle Scholar
  2. 2.
    Al-Suwailem, S. (2014). Complexity and endogenous instability. Research in International Business and Finance, 30, 393–410.CrossRefGoogle Scholar
  3. 3.
    Arrow, K., & Debreu, G. (1954). The existence of an equilibrium for a competitive economy. Econometrica, 22, 265–89.CrossRefGoogle Scholar
  4. 4.
    Barrow, J. (1998). Impossibility: The limits of science and the science of limits. Oxford: Oxford University Press.Google Scholar
  5. 5.
    Barwise, J. (1989). The situation in logic. Stanford, CA: Center for the Study of Language and Information.Google Scholar
  6. 6.
    Barwise, J., & Moss, L. (1996). Vicious circles. Stanford, CA: Center for the Study of Language and Information.Google Scholar
  7. 7.
    Bays, T. (2014). Skolem’s paradox. In E. Zalta (Ed.), Stanford Encyclopedia of Philosophy. Stanford, CA: Stanford University, https://plato.stanford.edu/.Google Scholar
  8. 8.
    Bergstra, J. A., & Middelburg, C. A. (2011). Preliminaries to an investigation of reduced product set finance. Journal of King Abdulaziz University: Islamic Economics, 24, 175–210.Google Scholar
  9. 9.
    Bernstein, P. (1996). Against the Gods: The remarkable story of risk. New York: Wiley.Google Scholar
  10. 10.
    Bernstein, P. (2007). Capital ideas evolving. New York: Wiley.Google Scholar
  11. 11.
    Bernstein, P. (2007). Capital ideas: Past, present, and future. In Lecture delivered at CFA Institute Annual Conference.Google Scholar
  12. 12.
    Berto, F. (2009). There’s something about Gödel: The complete guide to the incompleteness theorem. Hoboken: Wiley-Blackwell.CrossRefGoogle Scholar
  13. 13.
    Blaug, M. (1992). The methodology of economics. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  14. 14.
    Blaug, M. (1999). The disease of formalism, or what happened to neoclassical economics after war. In R. Backhouse & J. Creedy (Eds.), From classical economics to the theory of the firm (pp. 257–80). Northampton, MA: Edward Elgar.Google Scholar
  15. 15.
    Blaug, M. (2002). Is there really progress in economics? In S. Boehm, C. Gehrke, H. Kurz, & R. Sturm (Eds.), Is there progress in economics? European Society for the History of Economic Thought (pp. 21–41). Northampton, MA: Edward Elgar.Google Scholar
  16. 16.
  17. 17.
    Bookstaber, R. (2007). A demon of our own design. New York: Wiley.Google Scholar
  18. 18.
    Bookstaber, R., & Langsam, J. (1985). On the optimality of coarse behavior rules. Journal of Theoretical Biology, 116, 161–193.CrossRefGoogle Scholar
  19. 19.
    Bolander, T. (2002). Self-reference and logic. Φ News, 1, 9–44. http://phinews.ruc.dk/.
  20. 20.
    Bolander, T. (2014). Self-reference. In E. Zalta (Ed.), Stanford Encyclopedia of Philosophy. Stanford, CA: Stanford University, https://plato.stanford.edu/.Google Scholar
  21. 21.
    Bordo, M., Eichengreen, B., Klingebiel, D., & Martinez-Peria, M. S. (2001). Is the crisis problem growing more severe? Economic Policy, 32, 53–82.Google Scholar
  22. 22.
    Bouchaud, J. P. (2008). Economics needs a scientific revolution. Nature, 455, 1181.CrossRefGoogle Scholar
  23. 23.
    Breit, W., & Hirsch, B. (Eds.). (2009). Lives of the laureates (5th ed.). Cambridge, MA: MIT Press.Google Scholar
  24. 24.
    Byers, W. (2007) How mathematicians think: Using ambiguity, contradiction, and paradox to create mathematics. Princeton: Princeton University Press.Google Scholar
  25. 25.
    Byers, W. (2011). The blind spot: Science and the crisis of uncertainty. Princeton: Princeton University Press.CrossRefGoogle Scholar
  26. 26.
    Calude, C., Jurgensen, H., & Zimand, M. (1994). Is independence an exception? Applied Mathematical Computing, 66, 63–76.Google Scholar
  27. 27.
    Cassidy, J. (2009). How markets fail: The logic of economic calamities. New York: Farrar, Straus, and Giroux.Google Scholar
  28. 28.
    Chaitin, G., Doria, F. A., & da Costa, N. C. A. (2011). Gödel’s way: Exploits into an undecidable world. Boca Raton, FL: CRC Press.Google Scholar
  29. 29.
    Chrystal, K. A., & Mizen, P. D. (2003). Goodhart’s law: Its origins, meaning and implications for monetary policy. In P. Mizen (Ed.), Central banking, monetary theory and practice: Essays in honour of Charles Goodhart (Vol. 1). Northampton, MA: Edward Elgar.Google Scholar
  30. 30.
    Clower, R. (1995). Axiomatics in economics. Southern Economic Journal, 62, 307–319.CrossRefGoogle Scholar
  31. 31.
    Colander, D., Goldberg, M., Haas, A., Juselius, K., Kirman, A., Lux, T., & Sloth, B. (2009). The financial crisis and the systemic failure of the economics profession. Critical Review, 21, 249–67.CrossRefGoogle Scholar
  32. 32.
    Coleman, T. (2011). A practical guide to risk management. Charottesville, VA: CFA Institute.Google Scholar
  33. 33.
    Collins, H. (2010). Tacit and explicit knowledge. Chicago: University of Chicago Press.CrossRefGoogle Scholar
  34. 34.
    da Costa, N. C. A., & Doria, F. A. (1991). Undecidability and incompleteness in classical mechanics. International Journal of Theoretical Physics, 30, 1041–1073.CrossRefGoogle Scholar
  35. 35.
    da Costa, N. C. A., & Doria, F. A. (1992). On the incompleteness of axiomatized models for the empirical sciences. Philosophica, 50, 73–100.Google Scholar
  36. 36.
    da Costa, N. C. A., & Doria, F. A. (2005). Computing the future. In K. Velupillai (Ed.), Computability, Complexity and Constructivity in Economic Analysis. Malden, MA: Blackwell Publishers.Google Scholar
  37. 37.
    Davis, M. (2000). Engines of logic. New York: W.W. Norton.Google Scholar
  38. 38.
    DeLong, H. (1970). A profile of mathematical logic. Reading, MA: Addison-Wesley.Google Scholar
  39. 39.
    Dyson, F. (2006). The scientist as rebel. New York: New York Review Books.Google Scholar
  40. 40.
    Erickson, J. (2015). Models of computation. University of Illinois, Urbana-Champaign. http://jeffe.cs.illinois.edu Google Scholar
  41. 41.
    Etzioni, A. (1988). The moral dimension: Toward a new economics. New York: The Free Press.Google Scholar
  42. 42.
    Ferreirós, J. (2008). The crisis in the foundations in mathematics. In T. Gowers (Ed.), The Princeton companion to mathematics (pp. 142–156). Princeton: Princeton University Press.Google Scholar
  43. 43.
    Feyerabend, P. (2010). Against the method (4th ed.). London: Verso.Google Scholar
  44. 44.
    Filimonov, V., Bicchetti, D., Maystre, N., & Sornette, D. (2013). Quantification of the high level of endogeneity and of structural regime shifts in commodity markets. The Journal of International Money and Finance, 42, 174–192.CrossRefGoogle Scholar
  45. 45.
    Filimonov, V., & Sornette, D. (2012). Quantifying reflexivity in financial markets: Towards a prediction of flash crashes. Physical Review E, 85(5), 056108.CrossRefGoogle Scholar
  46. 46.
    Franzen, T. (2004). Inexhaustibility. Boca Raton: CRC Press.Google Scholar
  47. 47.
    Frydman, R., & Goldberg, M. (2007). Imperfect knowledge economics: Exchange rates and risk. Princeton: Princeton University Press.Google Scholar
  48. 48.
    Frydman, R., & Goldberg, M. (2011). Beyond mechanical markets: Asset price swings, risk, and the role of state. Princeton: Princeton University Press.CrossRefGoogle Scholar
  49. 49.
    FSA. (2009). The Turner review. London: Financial Services Authority.Google Scholar
  50. 50.
    Gleiser, M. (2014). The island of knowledge: The limits of science and the search for meaning. New York: Basic Books.Google Scholar
  51. 51.
    Gödel, K. (1931). Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I (On formally undecidable propositions of Principia Mathematica and related systems I). Monatshefte für Mathematik und Physik, 38, 173–198.CrossRefGoogle Scholar
  52. 52.
    Gödel, K. (1947). What is Cantor’s continuum problem? American Mathematical Monthly, 54, 515–525.CrossRefGoogle Scholar
  53. 53.
    Gödel, K. (1995). Some basic theorems on the foundations of mathematics and their implications. In S. Feferman (Ed.), Kurt Gödel Collected Works, Volume III: Unpublished essays and lectures (pp. 304–323). Oxford: Oxford University Press.Google Scholar
  54. 54.
    Goleman, D. (2006). Social intelligence. New York: Bantam Books.Google Scholar
  55. 55.
    Gray, J. (2008). Thoralf Skolem. In T. Gowers (Ed.), The Princeton companion to mathematics (pp. 806–807). Princeton: Princeton University Press.Google Scholar
  56. 56.
    Harcourt, G. (2003). A good servant but a bad master. In E. Fullbrook (Ed.), The crisis in economics. London: Routledge.Google Scholar
  57. 57.
    Hawking, S. (2002). Gödel and the end of the universe. www.hawking.org.uk.Google Scholar
  58. 58.
    Heiner, R. (1983). The origin of predictable behaviour. American Economic Review, 73, 560–595.Google Scholar
  59. 59.
    Keynes, J. M. (1936/1953). The general theory of employment, interest and money. San Diego: Harcourt Brace Jovanovich.Google Scholar
  60. 60.
    King, M. (2016). The end of alchemy. New York: W.W. Norton.Google Scholar
  61. 61.
    Kirman, A. (2012). The economy and the economic theory in crisis. In D. Coyle (Ed.), What’s the use of economics? Teaching the dismal science after the crisis. London: London Publishing Partnership.Google Scholar
  62. 62.
    Kline, M. (1980). Mathematics: The loss of certainty. Oxford: Oxford University Press.Google Scholar
  63. 63.
    Knight, F. (1921). Risk, uncertainty, and profit. New York: Houghton-Mifflin.Google Scholar
  64. 64.
    Kremer, P. (2014). The revision theory of truth. In E. Zalta (Ed.), Stanford Encyclopedia of Philosophy. Stanford, CA: Stanford University, https://plato.stanford.edu/.Google Scholar
  65. 65.
    Krugman, P. (2009, September 2). How did economists get it so wrong? New York Times.Google Scholar
  66. 66.
    Laplace, P. S. (1902/1951). A philosophical essay on probabilities. Translated into English from the original French 6th ed. by F.W. Truscott & F.L. Emory. New York: Dover Publications.Google Scholar
  67. 67.
    Lavoie, D. (1986). The market as a procedure for discovery and conveyance of inarticulate knowledge. Comparative Economic Studies, 28, 1–19.Google Scholar
  68. 68.
    Leonard, R. (1994). Money and language. In J. L. Di Gaetani (Ed.), Money: Lure, lore, and literature (pp. 3–13). London: Greenwood Press.Google Scholar
  69. 69.
  70. 70.
    Lieberman, M. (2013). Social: Why our brains are wired to connect. New York: Crown Publishers.Google Scholar
  71. 71.
    Lloyd, S. (2006). Programming the universe. New York: Vintage Books.Google Scholar
  72. 72.
    Lloyd, S. (2013). A Turing test for free will. Cambridge, MA: MIT Press. http://arxiv.org/abs/1310.3225v1.Google Scholar
  73. 73.
    Machtey, M., & Young, P. (1979). An introduction to the general theory of algorithms. New York: North–Holland.Google Scholar
  74. 74.
    Mainelli, M., & Giffords, B. (2009). The road to long finance: A systems view of the credit scrunch. London: Centre for the Study of Financial Innovation. Heron, Dawson & Sawyer. www.csfi.org.uk.Google Scholar
  75. 75.
    Marks, R. (2013). Learning lessons? The global financial crisis five years on. Journal and Proceeding of the Royal Society of New South Wales, 146, 3–16, A1–A43.Google Scholar
  76. 76.
    McCauley, J. (2012). Equilibrium versus market efficiency: Randomness versus complexity in finance markets. In S. Zambelli & D. George (Eds.), Nonlinearity, complexity and randomness in economics (pp. 203–210). Malden, MA: Wiley-Blackwell.CrossRefGoogle Scholar
  77. 77.
    Mintzberg, H. (1994). The rise and fall of strategic planning. New York: The Free Press.Google Scholar
  78. 78.
    Mishkin, F. (2007). The economics of money, banking, and financial markets (Alternate edition). New York: Pearson.Google Scholar
  79. 79.
    Nocera, J. (2009, January 2). Risk mismanagement. The New York Times.Google Scholar
  80. 80.
    North, D. (1990). Institutions, institutional change and economic performance. Cambridge, MA: Cambridge University Press.CrossRefGoogle Scholar
  81. 81.
    Polanyi, M. (1966). The tacit dimension. New York: Doubleday.Google Scholar
  82. 82.
    Popper, K. (1956/1988). The open universe: An argument for indeterminism. London: Routledge.Google Scholar
  83. 83.
    Priest, G. (1994). The structure of the paradoxes of self-reference. Mind, 103, 25–34.CrossRefGoogle Scholar
  84. 84.
    Priest, G. (2000). Beyond the limits of thought (2nd ed.). Oxford: Oxford University Press.Google Scholar
  85. 85.
    Putnam, H. (1967). Psychophysical predicates. In W. Capitan & D. Merrill (Eds.), Art, mind, and religion. Pittsburgh: University of Pittsburgh Press.Google Scholar
  86. 86.
    Rajan, U., Seru, A., & Vig, V. (2015). The failure of models that predict failures: Distance, incentives, and defaults. Journal of Financial Economics, 115, 237–260.CrossRefGoogle Scholar
  87. 87.
    Reinhart, C., & Rogoff, K. (2009). This time is different: Eight centuries of financial folly. Princeton: Princeton University Press.Google Scholar
  88. 88.
    Rice, H. G. (1953). Classes of recursively enumerable sets and their decision problems. Transactions of the American Mathematical Society, 74, 358–366.CrossRefGoogle Scholar
  89. 89.
    Rogers, H., Jr. (1967). Theory of recursive functions and effective computability. New York: McGraw-Hill.Google Scholar
  90. 90.
    Rosser, J. B. (2001) Alternative Keynesian and post Keynesian perspectives on uncertainty and expectations. Journal of Post Keynesian Economics, 23, 545–66.CrossRefGoogle Scholar
  91. 91.
    Rubinstein, A. (1998). Modeling bounded rationality. Cambridge, MA: MIT Press.Google Scholar
  92. 92.
    Savin, N., & Whitman, C. (1992). Lucas critique. In P. Newman, M. Milgate, & J. Eatwell (Eds.), New Palgrave dictionary of money and finance. New York: Palgrave.Google Scholar
  93. 93.
    Shiller, R. (2009). Irrational exuberance. Princeton: Princeton University Press.Google Scholar
  94. 94.
    Simon, H. (1978). Rationality as process and as product of thought. American Economic Review, 68, 1–16.Google Scholar
  95. 95.
    Simon, H. (1978/1992). Rational decision-making in business organizations. In A. Lindbeck (Ed.), Nobel Lectures, Economics 1969–1980 (pp. 343–371). Singapore: World Scientific Publishing Co. https://www.nobelprize.org.Google Scholar
  96. 96.
    Soros, G. (2003). Alchemy of finance. Hoboken: Wiley.Google Scholar
  97. 97.
    Soros, G. (2009, October 26). The general theory of reflexivity. Financial Times.Google Scholar
  98. 98.
    Sornette, D. (2003). Why stock markets crash: Critical events in complex financial systems. Princeton: Princeton University Press.Google Scholar
  99. 99.
    Sornette, D., & Cauwels, P. (2012). The illusion of the perpetual money machine. Notenstein Academy White Paper Series. Zurich: Swiss Federal Institute of Technology. http://arxiv.org/pdf/1212.2833.pdf.
  100. 100.
    Stewart, I. (1991). Deciding the undecidable. Nature, 352, 664–665.CrossRefGoogle Scholar
  101. 101.
    Stuart, T. (2013). Understanding computation. Beijing: O’Reilly.Google Scholar
  102. 102.
    Svozil, K. (1993). Randomness and undecidability in physics. Singapore: World Scientific.CrossRefGoogle Scholar
  103. 103.
    Svozil, K. (1996). Undecidability everywhere? In A. Karlqvist & J.L. Casti (Eds.), Boundaries and barriers: On the limits to scientific knowledge. Reading, MA: Addison-Wesley, pp. 215–237. http://arxiv.org/abs/chao-dyn/9509023v1.Google Scholar
  104. 104.
    Taleb, N. (2007). The black swan. New York: Random House.Google Scholar
  105. 105.
    Taleb, N. (2012). Antifragile. New York: Random House.Google Scholar
  106. 106.
    Trichet, J.-C. (2009). A paradigm change for the global financial system. BIS Review, 4/2009.Google Scholar
  107. 107.
    Tsuji, M., Da Costa, N. C. A., & Doria, F. A. (1998). The incompleteness of theories of games. Journal of Philosophical Logic, 27, 553–568.CrossRefGoogle Scholar
  108. 108.
    Tuckett, D. (2011). Minding the market: An emotional finance view of financial instability. Basingstoke: Palgrave MacMillan.CrossRefGoogle Scholar
  109. 109.
    Turing, A. (1936). On computable numbers, with an application to the Entscheidungsproblem. Proceedings of the London Mathematical Society, Series, 2(42), 230–265.Google Scholar
  110. 110.
    Velupillai, K. V. (2000). Computable economics. Oxford: Oxford University Press.CrossRefGoogle Scholar
  111. 111.
    Velupillai, K. V. (2012). Introduction. In K. V. Velupillai et al. (Eds.), Computable economics. International Library of Critical Writings in Economics. Northampton, MA: Edward Elgar.Google Scholar
  112. 112.
    Velupillai, K. V., Zambelli, S., & Kinsella, S. (Eds.). (2012). Computable economics. International Library of Critical Writings in Economics. Northampton, MA: Edward Elgar.Google Scholar
  113. 113.
    Wiltbank, R., Dew, N., Read, S., & Sarasvathy, S. D. (2006). What to do next? A case for non-predictive strategy. Strategic Management Journal, 27, 981–998.CrossRefGoogle Scholar
  114. 114.
    Winrich, J. S. (1984). Self-reference and the incomplete structure of neoclassical economics. Journal of Economic Issues, 18, 987–1005.CrossRefGoogle Scholar
  115. 115.
    Wolpert, D. (2008). Physical limits of inference. Physica, 237, 1257–1281.Google Scholar
  116. 116.
    Yanofsky, N. (2003). A universal approach to self-referential paradoxes, incompleteness and fixed points. The Bulletin of Symbolic Logic, 9, 362–386.CrossRefGoogle Scholar
  117. 117.
    Yanofsky, N. (2013). The outer limits of reason: What science, mathematics, and logic cannot tell us. Cambridge, MA: MIT Press.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Sami Al-Suwailem
    • 1
    Email author
  • Francisco A. Doria
    • 2
  • Mahmoud Kamel
    • 3
  1. 1.Islamic Development Bank GroupJeddahSaudi Arabia
  2. 2.Advanced Studies Research GroupPEP/COPPE, Federal University at Rio de JaneiroRio de JaneiroBrazil
  3. 3.College of Computer ScienceKing Abdul-Aziz UniversityJeddahSaudi Arabia

Personalised recommendations