Financial Mathematics
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Research Areas. Current research interests of some of the listed mathematics faculty are:
Prof. Goncharov’s research area is interest rate and credit risk derivatives. Currently, he concentrates on mortgage modeling. Based on an intensity-based approach to modeling prepayment rates, he works on development of various aspects of prepayment modeling, new approaches to model borrower’s refinancing incentive, valuation and hedging of mortgage pass-through securities and colateralized mortgage obligations. Another of his projects is a study of the exogenous mortgage rates.
Prof. Kercheval works in financial mathematics and mathematical economics, including: the dynamics of agent-based economic pricing models; portfolio and credit risk, including the use of non-gaussian modeling distributions; fixed income risk models; and financial problems in stochastic impulse control and numerical linear algebra. He has a background in geometric analysis and dynamical systems, and before coming to FSU worked in the financial industry on fixed income risk modeling.
Prof. Kim is interested in bond market modeling using probabilistic methods. One interesting choice of volatility for forward interest rates within an HJM model is an affine function of forward interest rates. Kim is trying to understand bond price dynamics obtained from various choices of volatility for forward interest rates. Currently, she is focusing on understanding the distribution of the time integral of a function of Geometric Brwoninan motion, which is related to pricing path dependent derivatives, e.g. as in Asian options.
Prof. Kopriva works in computational mathematics with interests in both the development and implementation of numerical algorithms. In particular, he develops highly accurate numerical solution methods for partial differential equation models. Previous work includes development of methods for and applications in hypersonic flows, compressible aerodynamics, aeroacoustics and electromagnetism.
Prof. Nichols has a broad range of interests within financial mathematics, focusing on probabilistic methods and on the interplay between discrete and continuous models. His interests include the pricing and hedging of financial derivatives, mortgages, portfolio management, and financial problems which incorporate a long time horizon.
Prof. Nolder’s research interests include agent-based economic systems, random dynamical systems and stochastic equilibria, evolutionary finance, game theory, stochastic portfolio theory and evolutionary portfolio theory. Other interests include asset and option pricing using exponential Levy and additive models, time-changed processes and especially selfsimilar additive models. Involved are the calibration of models, simulations to price exotic options and maximum and quasi likelihood methods. Nolder also remains active in his previous research areas: recent publications involve systems of conjugate harmonic functions in Clifford algebras and quasiregular mappings in Carnot groups; he is interested in the Apollonian metric on Carnot groups and stochastic processes on Carnot groups.
Prof. Ökten is interested in computational finance and Monte Carlo & quasi-Monte Carlo methods. His recent research is on (a) the design of effective simulation techniques for high dimensional problems in security pricing, (b) randomized quasi-Monte Carlo methods and their use in computational finance, and (c) quasi-Monte Carlo error bounds in financial problems and statistical accuracy of different normal variate generation techniques in the context of low-discrepancy sequences.
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