Raphael Douady

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Raphael Douady
Born15 November 1959 (1959-11-15) (age 64)
Paris, France
Alma materÉcole normale supérieure
Scientific career
Doctoral advisorMichael Herman

Raphael Douady (born 15 November 1959) is a French mathematician and economist. He holds the Robert Frey Endowed Chair for Quantitative Finance at Stony Brook, New York. He is a fellow of the Centre d’Economie de la Sorbonne (Economic Centre of Sorbonne), Paris 1 Pantheon-Sorbonne University, and academic director of the Laboratory of Excellence on Financial Regulation (Labex Refi).

Early life and education[edit]

Douady is the son of mathematician Adrien Douady (1935–2006). He is an alumnus of Ecole Normale Supérieure, where he placed first in the entrance exam. He later ranked first in the Agrégation de mathématiques in 1980. He earned his PhD in the fields of Hamiltonian systems in 1982 at the Paris Diderot University (Paris 7), while still a student at ENS, under the guidance of Michael Herman.[citation needed]


In 1983, Douady was appointed to the Centre National de la Recherche Scientifique (CNRS). He was affiliated with Ecole Polytechnique (1983–87), Ecole Normale Supérieure (1987–95), the Courant Institute at New York University (1995–97), Ecole Normale Supérieure of Cachan (1997–2001), and a former visiting professor at New York University Polytechnic Institute.[1] In 2001, he founded Riskdata, a private software company, remaining with them until 2011 since when he has been affiliated to Paris 1 Pantheon-Sorbonne University.

In 1994, he created and animated the Bachelier Seminar of mathematical finance at Institut Henri Poincaré in Paris. He is also the co-founder, with Marco Avellaneda, of the Seminar of Mathematical Finance held at the Courant Institute of Mathematical Science, New York University. He has advised financial institutions including Société Générale, National Westminster Bank, Canadian Imperial Bank of Commerce and Citibank.[citation needed]

In 1999, along with Ingmar Adlerberg, a computer scientist from the French Institute for Research in Computer Science and Automation (INRIA) and the Massachusetts Institute of Technology (MIT), Douady co-founded Riskdata, a company producing risk management software that helps buy-side financial institutions leading a proactive risk management and complying with financial regulations. He continues to be involved as their research director.[citation needed]

In 2013, Douady was appointed as academic director of the Laboratory of Excellence on Financial Regulation (Labex refi),[2] where his role was to supervise approximately sixty researchers on the inter-relations between financial regulations, the financial system and the real economy, and to advise governments and regulators on these issues. In 2015, he was appointed Frey Family[3] endowed chair professor of quantitative finance at State University of New York in Stony Brook University. His role is to lead the graduate program in quantitative finance, initially created by Robert J. Frey.[citation needed]

Notable research[edit]

Douady worked on the Kolmogorov–Arnold–Moser (KAM) theorem on the existence of invariant tori in Hamiltonian systems. In his PhD thesis he proved the equivalence of KAM theory for Hamiltonian systems and for symplectomorphisms, opening the gate to discrete KAM theory.[4] He contributed to the theory of outer billiards, providing a full proof of a result announced earlier by J. Moser.

Douady is the author of a seminal article in 1988 on Arnold diffusion,[5] where he proved a long-standing conjecture of Vladimir Arnold on the existence of topologically unstable elliptic orbits of Hamiltonian systems in dimensions greater than or equal to 6.[6]

In 1999, he established with Jean-Christophe Yoccoz a theory of automorphic measures of circle diffeomorphisms, a basis for differentiating the rotation number function.[7]

Since 1994, Douady has conducted research in the field of mathematical finance, statistics and economics. He established a generalization of Heath–Jarrow–Morton interest rate model, where the yield curve is represented as a random field.[8] With Monique Jeanblanc, he created a rating-based credit derivatives model that introduced the notion of "rating surface".[9] In collaboration with Albert Shiryaev and Marc Yor he co-authored a theory of Brownian motions downfalls.[10]

Douady has concentrated research on financial instabilities, nonlinearities and systemic risk. He developed a statistical theory, called "polymodels" to compute an anticyclical risk indicator, the "Stress VaR", a more extended version of the Basel III stress tests.[11] In a book co-authored with Thomas Barrau, he demonstrated that polymodels are applicable to a wide range of problems in finance, especially the question of predicting the stock market.[12] Inspired by Minsky's financial instability hypothesis, he proposed a Market Instability Indicator based on the first Lyapunov exponent of flows of funds evolution.[13] In collaboration with Nassim Nicholas Taleb he developed the mathematical foundations of "fragility/antifragility" theory.[14]



  1. ^ "Raphael Douady". mbfasorbonne.univ-paris1.fr. Archived from the original on 6 March 2014.
  2. ^ See http://www.labex-refi.com
  3. ^ "Frey Family Foundation Establishes $1.5M Endowed Chair in Quantitative Finance at Stony Brook University". commcgi.cc.stonybrook.edu. Archived from the original on 15 May 2008.
  4. ^ See Wiggins, S. (2003). Introduction to Applied Nonlinear Dynamical Systems and Chaos. Springer. ISBN 9780387001777.
  5. ^ Douady, R. (1988). "Stabilité ou instabilité des points fixes elliptiques" (PDF). Annales Scientifiques de l'École Normale Supérieure. 4ème série. 21 (1): 1–46. doi:10.24033/asens.1549.
  6. ^ See Arnold’s Problems, problem 1963-1, Springer, 2004 http://www.lavoisier.fr/livre/notice.asp?ouvrage=2294531
  7. ^ Douady, R.; Yoccoz, J.-C. (1999). "Rotation number of diffeomorphisms of the circle and automorphic measures". Regul. Chaotic Dyn. 4 (4): 19–38. doi:10.1070/rd1999v004n04ABEH000129. Archived from the original on 10 November 2013.
  8. ^ Douady, R (2014). "Yield Curve Smoothing and Residual Variance of Fixed Income Positions". Inspired by Finance (PDF). Vol. 2013. pp. 221–256. doi:10.1007/978-3-319-02069-3_10. ISBN 978-3-319-02068-6. S2CID 56055127.
  9. ^ Douady, R.; Jeanblanc, M. A (2002). "Rating-based Model for Credit Derivatives". European Investment Review. 1: 17–29. CiteSeerX
  10. ^ Douady, R.; Shiryaev, A.N.; Yor (2000). "Downfalls" in a Standard Brownian Motion Theory". Probab. Appl. 44 (1): 29–38. doi:10.1137/S0040585X97977306.
  11. ^ Coste, C.; Douady, R.; Zovko, I. (2011). "The StressVaR: A New Risk Concept for extreme Risk and Fund Allocation, the Journal of Alternative Investments" (PDF). The Journal of Alternative Investments. 13 (3): 10–23. doi:10.3905/jai.2011.13.3.010. S2CID 155028269.
  12. ^ Barrau, Thomas; Douady, Raphael (2022). Financial Mathematics and Fintech, Springer Nature (ed.). Artificial Intelligence for Financial Markets: The Polymodel Approach. Financial Mathematics and Fintech. doi:10.1007/978-3-030-97319-3. ISBN 978-3-030-97318-6. S2CID 249247177.
  13. ^ Douady, R.; Choi, Y. (2013). "Financial Crisis and Contagion: A Dynamical Systems Approach". In Fouque, J. P.; Langsam, J. A. (eds.). Handbook on Systemic Risk. Cambridge University Press.
  14. ^ Taleb, N. N.; Douady, R. (2013). "Mathematical Definition, Mapping, and Detection of (Anti)Fragility". Quantitative Finance. 13 (11): 1677–1689. arXiv:1208.1189. doi:10.1080/14697688.2013.800219. S2CID 219716527. SSRN 2124595.
  15. ^ "International Mathematical Olympiad".