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 in Paris) is a French mathematician and economist at Centre d’Economie de la Sorbonne, Paris Sorbonne University, an invited professor at New York University Polytechnic Institute,[1] and academic director of the Laboratory of Excellence on Financial Regulation.

Biography

He is the son of Adrien Douady (1935–2006), mathematician, and member of the Bourbaki group.

Douady is a former student of Ecole Normale Supérieure where he ranked first at the entrance exam in 1978 and at 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.

He was appointed in 1983 by the CNRS (Centre National de la Recherche Scientifique). He was affiliated with Ecole Polytechnique (1983–87), Ecole Normale Supérieure (1987–95), New York University Courant Institute (1995–97), Ecole Normale Supérieure of Cachan (1997–2001), Riskdata (private software company, 2001–11) and Paris 1 Pantheon-Sorbonne University since 2011.

Dynamical systems

Raphael Douady worked on so-called 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 lasting conjecture of Vladimir Arnold on the existence of topologically unstable elliptic orbits of Hamiltonian systems in dimension 6 and over.[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, Raphael Douady turned his research to 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, introducing the notion of “rating surface”. [7] He has authored with Albert Shiryaev and Marc Yor a theory of Brownian motions downfalls.[8] He created in 1994 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 of the Courant Institute of Mathematical Science (New York University). He has advised financial institutions such as Société Générale, National Westminster, Canadian Imperial Bank of Commerce and Citibank.

Statistics and economics

From his dynamical systems background, Raphael Douady stays permanently concerned with 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 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] He worked out with Nassim Nicholas Taleb the mathematical foundations of “fragility/antifragility” theory.[11]

Entrepreneurship

In 1999, Raphael Douady co-founded Riskdata with Ingmar Adlerberg, a computer scientist from INRIA and MIT, a risk management software company helping buy-side financial institutions comply with financial regulations and remains its research director.

Academic appointment at Labex ReFi

In 2013, he has been appointed as academic director of the Laboratory of Excellence on Financial Regulation (Labex refi),[12] where his role is to supervise research of ca. 60 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"