Research interests
Monte carlo methods.

Giray Ökten received an undergraduate degree in Mathematics from Bogazici University, Turkey, in 1991, a Master's in 1994, and a PhD in Mathematics in 1997 from Claremont Graduate University, California. He joined Florida State University in 2005 and served as Director of Financial Mathematics from 2008 to 2012, and Associate Chair for Graduate Studies from 2012 to 2015.

Prof. Ökten is interested in the theory of Monte Carlo and quasi-Monte Carlo methods, and computational finance. Monte Carlo methods are numerical tools that are used in sciences and engineering. They use random numbers to simulate a complex system, and the result of the simulation gives an approximate answer to the problem at hand. Quasi-Monte Carlo methods, on the other hand, try to solve similar problems as Monte Carlo, but with one important difference: quasi-Monte Carlo methods use some deterministically generated sequences, called low-discrepancy sequences, instead of random numbers in simulation. Usually, the quasi-Monte Carlo method provides more accurate estimates than Monte Carlo, however, it has its own limitations.

A substantial part of Dr. Ökten's research lies in the development of Monte Carlo algorithms, and the development of hybrid sequences that combine random and low-discrepancy sequences, in order to get the best features of Monte Carlo and quasi-Monte Carlo worlds. An example of such hybrid methods is the "mixed sequence", where a low-discrepancy sequence is concatenated with a random sequence. Another hybrid method is the development of the sequence "rasrap". Dr. Ökten has also published some papers in parallel (randomized) quasi-Monte Carlo sequences, and applications in engineering.

Giray Okten
Giray Ökten
Professor of Mathematics
Selected papers
Salehy, N., Ökten, G. (2021) Dempster-Shafer Theory for Stock Selection. IEEE 45th Annual Computers, Software, and Applications Conference (COMPSAC), July 12-16, 2021.
Fox, J., Ökten, G. (2021) Polynomial Chaos as a Control Variate Method. SIAM Journal on Scientific Computing, 43(3), pp A2268-A2294.
Fox, J., Ökten, G. (2021) Brownian Path Generation with Polynomial Chaos, SIAM Journal on Financial Mathematics, 12(2), pp 724-743.
Ökten, G., Shah, M., & Goncharov, Y. (2012). Random and Deterministic Digit Permutations of the Halton Sequence. In Lezsek Plaskota, & Henrik Wozniakowski (Eds.), 9th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, Warsaw, Poland, August 15-20, 2010 (pp. 589-602). Springer-Verlag Berlin Heidelberg.
Ökten, G., & Göncü , A. (2011). Generating low-discrepancy sequences from the normal distribution: Box-Muller or inverse transformation? Mathematical and Computer Modelling, 53, 1268-1281.
Ökten, G. (2009). Generalized von Neumann-Kakutani transformation and random-start scrambled Halton sequences. Journal of Complexity, 25, 4, 318-331.
Ökten, G., Salta, E., & Göncü , A. (2008). On Pricing Discrete Barrier Options Using Conditional Expectation and Importance Sampling Monte Carlo. Mathematical and Computer Modelling, 47, 484-494.
Goncharov, Y., Ökten, G., & Shah, M. (2007). Computation of the endogenous mortgage rates with randomized quasi-Monte Carlo simulations. Mathematical and Computer Modelling, 46, 459-481.
Department of Mathematics

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