Research interests
Monte Carlo methods for nonlinear PDEs, Financial Mathematics

Professor Fahim earned his PhD in Applied Mathematics in 2010 at the Centre de Mathematiques Appliquees, Ecole polytechnique, France, under the direction of Nizar Touzi. Prior to joining FSU he held a postdoctoral position at the University of Michigan in Ann Arbor. His primary research interest is "probabilistic numerical methods (Monte Carlo) for nonlinear partial differential equations with applications in finance". The main goal of this research is to obtain faster and more accurate algorithms for financial risk pricing in the Markovian (and occasionally non-Markovian) framework, especially in the presence of several risk sources. Dr. Fahim is now working on the extension of the Monte Carlo methods for more general partial differential equations and on their efficiency. Dr. Fahim has also done some research in the "homogenization of linear partial differential equations of divergence of with random coefficients" and in the "mathematical basis of quickest threat detection". The former research has application in many areas including modelling random media, and the latter area, in general, deals with optimal stopping problems.

Arash Fahim
Arash Fahim
Assistant Professor of Mathematics
Selected papers
Joseph Conlon and Arash Fahim, Strong convergence to the homogenized limit of elliptic equations with random coefficients II, Bull. London Math. Soc. first published online April 17, 2013.
Joseph Conlon and Arash Fahim, Strong convergence to the homogenized limit of parabolic equations with random coefficients, To appear in Transactions of the American Mathematical Society.
Erhan Bayraktar and Arash Fahim, A Stochastic Approximation for Fully Nonlinear Free Boundary Problems, Numerical Methods for Partial Differential Equations.
Arash Fahim, Nizar Touzi, and Xavier Warin, A probabilistic numerical method for fully non-linear parabolic PDEs, Annals of Applied Probability, 21(4):1322-1364.
Department of Mathematics

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Florida State University

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