1. ¹leads RaisePartner's Quantitative Research & Consulting Group. He holds a PhD in Systems Modelling & Control Theory from University Paris-IX Dauphine. Before co-founding RaisePartner, he served as CTO of Saphir Control, and prior to that he was a research fellow at INRIA.
2. ²is President CEO of RaisePartner. He holds a PhD in Optimization & Econometrics from University La Sorbonne (Paris I/ENSTA). Before founding RaisePartner, he was a research scientist at the French Institute for Computer Science and Control (INRIA). He also took Post-Doc Research positions at Courant Institute (New York University) and the Center of Operations Research and Econometrics (Louvain-La-Neuve).
3. ³is a senior consultant and quantitative analyst in RaisePartner's Quantitative Research and Consulting Group, where she develops risk and optimisation models for clients as well as for RaisePartner proprietary products. She holds a Masters in Materials Science and Engineering from University Grenoble Joseph Fourier of Grenoble.

Correspondence: Véronique Piolle, RaisePartner, 110 Boulevard Sebastopol, 75003, Paris, France, Tel: +33 4 3837 4380; e-mail:Veronique.Piolle@raisepartner.com

Revised 11 May 2006.

Abstract

One of the current challenges of risk modelling consists in building global risk models from local ones: from a set of local market risk forecasts (local covariance matrices) and cross-market correlations, a global covariance matrix preserving local market estimations and restoring a positive semidefinite matrix must be computed. Convex optimisation, taking advantage of the convex properties of dual functions, is an original and high-performing approach for such a process. In this paper, a particular semidefinite program is posed and solved with dual convex algorithms for correlation matrices in order to build a global risk model, starting from a set local market covariance, and cross-correlation. Some numerical illustrations are given.