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Arash Fahim

Contact info:

217 LOVE building
Department of Mathematics
Florida State University
1017 Academic Way
Tallahassee, FL 32306, USA

I 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 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) and Hua-Yi Lin (2018) and currently have a PhD student Kangwei Xing (projected to graduate on Fall 2019).

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 is now summarizing his findings on the theoretical aspects of robust hedging under liquidity constraints in to his thesis.

Research Interests:

  • Applied Probability
  • Monte Carlo Methods for PDEs
  • Financial Mathematics

Publications

A numerical scheme for a singular control problem: Investment-consumption under proportional transaction costs
W.-Y. Tsai and A. Fahim, Journal of Computational and Applied Mathematics,  333,  170-184,  (2018)
Optimal portfolio execution under time-varying liquidity constraints
H.-Y. Lin and A. Fahim, Applied Mathematical Finance,  24,  387-416,  (2017)
Volatility can be detrimental to option values!
H. Ghoddusi and A. Fahim, Economics Letters,  149,  5-9,  (2016)
Model-independent superhedging under portfolio constraints
A. Fahim and Y.-J. Huang, Finance and Stochastics,  20,  51-81,  (2016)
Long range correlation inequalities for massless Euclidean fields
J. G. Conlon and A. Fahim, Illinois Journal of Mathematics,  59,  143-187, 0019-2082,  (2015)
Strong convergence to the homogenized limit of parabolic equations with random coefficients
J. Conlon and A. Fahim, Transactions of the American Mathematical Society,  367,  3041-3093, 0002-9947,  (2015)
Strong convergence to the homogenized limit of elliptic equations with random coefficients II
J. G. Conlon and A. Fahim, Bulletin of the London Mathematical Society,  45,  973-986, 0024-6093,  (2013)
A stochastic approximation for fully nonlinear free boundary parabolic problems
E. Bayraktar and A. Fahim, Numerical Methods for Partial Differential Equations,  30,  902-929, 0749-159X,  (2014)
A probabilistic numerical method for fully nonlinear parabolic PDEs
A. Fahim and N. Touzi and X. Warin, The Annals of Applied Probability,  21,  1322-1364, 1050-5164,  (2011)




Preprints

Optimal investment in a dual risk model
A. Fahim and L. Zhu, arXiv preprint arXiv:1510.04924,  (2015)
Asymptotic analysis for optimal dividends in a dual risk model
A. Fahim and L. Zhu, arXiv preprint arXiv:1601.03435,  (2016)
Optimal production policy under the carbon emission market
A. Fahim and N. Touzi, (2015)




REU summer 2013 (With Michael Angileri)

Implementing a variation of Longstaff-Schwatz algorithm proposed by Bouchard and Warin
Student researcher: Micheal Angileri, University of Michigan

Header files

cpp files

Presentation slides

Bibliography:

Valuing American Options by Simulation: A Simple Least-Squares Approach
Francis A. Longstaff and Eduardo S. Schwartz, The Review of Financial Studies,  14, No. 1,  113-147,  (2001)
Monte-Carlo valorisation of American options: facts and new algorithms to improve existing methods
Bruno Bouchard and Xavier Warin, Numerical Methods in Finance, In: Carmona R., Del Moral P., Hu P., Oudjane N. (eds) Numerical Methods in Finance, Springer Proceedings in Mathematics,  12,  (2012)








Financial Mathematics at the Florida State University

The Department of Mathematics hosts and runs the program since 1998 with support from faculty members in Statistics, Economics, Finance, and Computer Science.

We offer both MS and PhD in financial mathematics to the students from all majors with an strong math background. For more information visit the program web page. The details of our graduate programs can be found at MS and PhD.