Raphael Douady

Raphael Douady
Born 1959
Paris, France
Nationality French
Fields Mathematics
Alma mater École normale supérieure
Doctoral advisor Michael Herman
Doctoral students Arnaud Trébaol

Raphael Douady (born November 15, 1959) is a French Mathematician and Economist, born in Paris. 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).

Biography

He is the son of Adrien Douady (1935–2006), one of the most prolific mathematician of the 20th century and member of the Bourbaki group.

Douady is a Valedictorian of Ecole Normale Supérieure, and earned 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.

In 1983, he 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.

Dynamical systems

Raphael 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.[2]

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,[3] 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.[4]

In 1999, he established with Jean-Christophe Yoccoz a theory of automorphic measures of circle diffeomorphims, a basis for differentiating the rotation number function.[5]

Mathematical finance

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 .[6] With Monique Jeanblanc, he created a rating-based credit derivatives model that introduced the notion of “rating surface”. [7] In collaboration with Albert Shiryaev and Marc Yor he co-authored a theory of Brownian motions downfalls.[8] 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 such as Société Générale, National Westminster Bank, Canadian Imperial Bank of Commerce and Citibank.

Statistics and economics

Starting from a background in dynamical systems Douady has concentrated research on financial instabilities, nonlinearities and systemic risk. He developed a statistical theory, called “polymodels” to compute an anticylical risk indicator, the “Stress VaR”, a more extended version of the Basel III stress tests. [9] Inspired by Minsky’s financial instability hypothesis, he proposed a Market Instability Indicator based on the first Lyapunov exponent of flows of funds evolution.[10] In collaboration with Nassim Nicholas Taleb he developed the mathematical foundations of “fragility/antifragility” theory.[11]

Entrepreneurship

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.

Academic appointment at Labex ReFi

In 2013, he was appointed as academic director of the Laboratory of Excellence on Financial Regulation (Labex refi),[12] 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.

Other activities and commitments

Awards

References

  1. ↑ http://mbfasorbonne.univ-paris1.fr/staff/douadyraphael.html
  2. ↑ See wiggins, S., Introduction to Applied Nonlinear Dynamical Systems, Springer, 2003
  3. ↑ Douady, R. Stabilité ou instabilité des points fixes elliptiques, Annales scientifiques de l’ENS, 4ème série, t. 21, n° 1 (1988), pp. 1–46 http://archive.numdam.org/ARCHIVE/ASENS/ASENS_1988_4_21_1/ASENS_1988_4_21_1_1_0/ASENS_1988_4_21_1_1_0.pdf
  4. ↑ See Arnold’s Problems, problem 1963-1, Springer, 2004 http://www.lavoisier.fr/livre/notice.asp?ouvrage=2294531
  5. ↑ Douady, R.;Yoccoz, J.-C. Rotation number of diffeomorphisms of the circle and automorphic measures Regul. Chaotic Dyn. 4 4 (1999) 19–38 http://ics.org.ru/eng?menu=mi_pubs&abstract=148
  6. ↑ Douady, R. Yield Curve Smoothing and Residual Variance of Fixed-income Positions in Inspired By Finance, The Musiela Festschrift, ed. Kabanov, Rutkowski, Zariphopoulou, Springer 2013, pp. 221–256 http://link.springer.com/chapter/10.1007/978-3-319-02069-3_10#page-1
  7. ↑ Douady, R., Jeanblanc, M. A Rating-based Model for Credit Derivatives European Investment Review, 1:17–29, 2002 http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.139.220
  8. ↑ Douady, R., Shiryaev, A.N., Yor, M. On Probability Characteristics of "Downfalls" in a Standard Brownian Motion Theory Probab. Appl., 44(1), 29–38 http://epubs.siam.org/doi/abs/10.1137/S0040585X97977306
  9. ↑ Coste, C., Douady, R., Zovko, I., The StressVaR: A New Risk Concept for extreme Risk and Fund Allocation, the Journal of Alternative Investments, Winter 2011, Vol. 13, No 3, pp. 10–23 http://www.iijournals.com/doi/abs/10.3905/jai.2011.13.3.010#sthash.Vg9wGF7W.vBBkyVoS.dpbs
  10. ↑ Douady, R., Choi, Y., Financial Crisis and Contagion: A Dynamical Systems Approach in Handbook on Systemic Risk, edited by J.P. Fouque and J.A. langsam, Cambridge University Press, 2013 http://www.cambridge.org/ar/academic/subjects/mathematics/optimization-or-and-risk-analysis/handbook-systemic-risk
  11. ↑ Taleb, N.N, Douady, R., Mathematical Definition, Mapping, and Detection of (Anti)Fragility, Quantitative Finance, 2013 http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2124595
  12. ↑ See http://www.labex-refi.com"
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