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    Abstract:

    We introduce a numerical methodology which applies to a broad class of partial differential equations and discrete models, and is referred to here as the transport-based mesh-free method. It led us to several numerical algorithms which are now implemented in a Python library, called CodPy. We develop a mesh-free discretization technique based on the (so-called RKHS) theory of reproducing kernels and the theory of transport mappings, in a way that is reminiscent of Lagrangian methods in computational fluid dynamics. The strategy is relevant when a large number of dimensions or degrees of freedom are present, as is the case in mathematical finance and machine learning, but is also applicable in fluid dynamics. We present our algorithms primarily for the Fokker-Planck-Kolmogorov system of mathematical finance and for neural networks based on support vector machines. The proposed algorithms are nonlinear in nature and enjoy quantitative error estimates based on the notion of discrepancy error, which allow one to evaluate the relevance and accuracy of given data and numerical solutions.

    Bio:

    Philippe G. LeFloch holds a permanent position at Sorbonne University, as a Research Professor of the Centre National de la Recherche Scientifique (CNRS). He graduated from the Ecole Normale Superieure (Saint- Cloud) and, in 1988, obtained a Ph.D. in Applied Mathematics from the Ecole Polytechnique (Palaiseau). In 1995, he received a Faculty Early Career Development award from the National Science Foundation. He worked at the Courant Institute of Mathematical Sciences (NY) and at the University of Southern California. P.G. LeFloch published about 250 research papers with more than 100 different co-authors, and several textbooks including graduate courses. For the past ten years he developed a new methodology for mathematical finance and data science, which led to the development of the CodPy algorithms.

Latest News

February 8th, 2021

Paul Glasserman Selected as the Recipient of the 2020 IAQF/Northfield Financial Engineer of the Year Award

The International Association for Quantitative Finance (IAQF) and Northfield Information Services have named Paul Glasserman, the Jack R. Anderson Professor of Business at Columbia University’s School of Business, the 2020 IAQF/Northfield Financial Engineer of the Year (FEOY). The award will be presented to Professor Glasserman at a celebration when it is safe to reconvene again.

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IAQF Senior Fellow Spotlight

                                                


Robert Jarrow

Robert Jarrow is a Professor at Cornell University and director of research at Kamakura Corporation. He is a creator of the Heath-Jarrow-Morton model, the forward price martingale measure, and reduced form credit risk models. His research was the first to distinguish forward/futures prices and study option pricing with market manipulation. He has been the recipient of numerous prizes and awards including the CBOE Pomerance Prize for Excellence in Options Research, the Graham and Dodd Scrolls Award, the Bernstein Fabozzi/Jacobs Levy Award, and the 1997 IAFE/SunGard Financial Engineer of the Year. In 2009 he was awarded Risk Magazine’s Lifetime Achievement Award. He is included in both the Fixed Income Analysts Society Hall of Fame and Risk Magazine’s 50 member Hall of Fame. He has written seven text books, including the first on the Black Scholes and HJM models, and has over 200 academic journal publications.

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