Arash Fahim

I earned my PhD in Applied Mathematics in 2010 at the Centre de Mathematiques Appliquèes, École Polytechnique, France, under the direction of Nizar Touzi. Prior to joining FSU I held a postdoctoral position at the University of Michigan in Ann Arbor. My thesis was on 'probabilistic numerical methods (Monte Carlo) for nonlinear partial differential equations with applications to finance'. The main goal of this research is to obtain faster and more accurate algorithms for financial risk pricing and hedging in the Markovian framework, especially in the presence of several risk sources. 

I have also done research in homogenization of linear random PDEs, robust finance, financial economics, and optimal execution of large market orders. I have graduated two PhD students, Wan-Yu Tsai (2017), Hua-Yi Lin (2018), Kangwei Xing (2020),  Hung Duong (2023), Arafatur Rahman  (projected 2024), and Changkui Wu (projected 2024).

Wan-Yu worked on a Monte Carlo algorithm for singular control problems such as the optimal investment-consumption under proportional transaction cost. Hua-Yi finish his dissertation on the optimal execution problem with time-varying liquidity constraints. Kangwei's dissertation  was  on the continuous-time robust hedging under portfolio constraints.  He used several new continuous-time techniques on the Skorokhod space under non-metrizable weak topologies. 

Arafatur is working on optimal execution under volatile limit order book and Hung's topic concerns  machine learning based numerical schemes techniques for fully nonlinear PDEs.