Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-24T00:23:55.286Z Has data issue: false hasContentIssue false
  • English
  • Français

Response to Johnson: A random sample versus the radical event

Published online by Cambridge University Press:  09 November 2023

Elie Ayache
Elie Ayache*
Affiliation:
ITO 33, France
*
Corresponding author: Elie Ayache, ITO 33, 36 rue Lacépède, 75005 Paris, France. Email: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Timothy Johnson's working hypothesis in his review of my latest book, The Medium of Contingency, is that I (as well as the ‘quants’ involved in the derivative pricing industry) do not understand the foundations of abstract probability theory. In this response, I show that this is not the case. On the contrary, rules and protocols which are common in the derivative pricing industry, the result of which can be an extension of abstract probability theory as it now stands, seem to elude Johnson. To address these failings, I provide theoretical reflections on probability theory and its formalisms.

Keywords

Abstract probability theoryrandom samplerandom variablecontingencyderivatives market
Type
Review forum
Information
Finance and Society , Volume 2 , Issue 2: Art and finance , 2016 , pp. 205 - 216
Creative Commons
Creative Common License - CCCreative Common License - BYCreative Common License - NCCreative Common License - ND
This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial-No Derivatives licence (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits noncommercial re-use, distribution, and reproduction in any medium, provided the original work is unaltered and is properly cited. The written permission of Cambridge University Press must be obtained for commercial re-use or in order to create a derivative work.
Copyright
© 2016 The Author(s)

References

Ayache, E. (2010) The Blank Swan: The End of Probability. Chichester: Wiley & Sons.Google Scholar
Ayache, E. (2015) The Medium of Contingency: An Inverse View of the Market. New York, NY: Palgrave Macmillan.CrossRefGoogle Scholar
Bergomi, L. (2016) Stochastic Volatility Modeling. Boca Raton, FL: CRC Press.Google Scholar
Bonitzer, J. (1984) Philosophie du Hasard. Paris: Éditions Sociales.Google Scholar
Hobson, D. (2011) The Skorokhod embedding problem and model-independent bounds for option prices. In: Carmona, R. (ed.) Paris-Princeton Lectures on Mathematical Finance 2010. New York, NY: Springer, 267–318.CrossRefGoogle Scholar
Johnson, T. (2010) What is financial mathematics? In: Pitici, M. (ed) The Best Writing on Mathematics 2010. Princeton, NJ: Princeton University Press, 43–46.Google Scholar
Johnson, T. (2016a) Sincerity - the subjective rationality of markets. Available at: <http://magic-maths-money.blogspot.fr/2016/01/sincerity-subjective-rationality-of.html/>. Accessed 31 August 2016..+Accessed+31+August+2016.>Google Scholar
Johnson, T. (2016b) The necessity of multi-disciplinary scholarship for finance: On Ayache and Roffe. Finance and Society, 2(2): 189–204.CrossRefGoogle Scholar
Meillassoux, Q. (2007) Potentiality and virtuality. Collapse: Philosophical Research and Development, II: 55–81.Google Scholar
Mugur-Schächter, M. (1992). The probability trees of quantum mechanics: Probabilistic meta-dependence and meta-meta-dependence. In: Carvallo, M.E. (ed) Nature, Cognition and System II. Dordrecht: Kluwer Academic Publishers, 89–111.CrossRefGoogle Scholar
Rebonato, R. (2004) Volatility and Correlation: The Perfect Hedger and the Fox. Chichester: Wiley & Sons.CrossRefGoogle Scholar
Shafer, G. and Vovk, V. (2001). Probability and Finance: It's Only a Game! Chichester: Wiley & Sons.CrossRefGoogle Scholar
Taleb, N.N. (2007) The Black Swan: The Impact of the Highly Improbable. New York, NY: Random House.Google Scholar
Tanaka, Y. (2013) The problem of the indeterminate past in quantum physics and Whitehead's epochal theory of time. Available at: <http://pweb.sophia.ac.jp/process/>. Accessed 31 August 2016.. Accessed 31 August 2016.' href=https://scholar.google.com/scholar?q=Tanaka,+Y.+(2013)+The+problem+of+the+indeterminate+past+in+quantum+physics+and+Whitehead's+epochal+theory+of+time.+Available+at:+.+Accessed+31+August+2016.>Google Scholar
Tao, T. (2010) 254A, Notes 0: A review of probability theory. Available at: <https://terrytao.wordpress.com/2010/01/01/254a-notes-0-a-review-of-probability-theory/>. Accessed 31 August 2016..+Accessed+31+August+2016.>Google Scholar