Probability, Stochastic Processes and Financial Mathematics
Probability theory, a well-established branch of mathematics, provides the mathematical framework for the study of random phenomena arising in nature and many aspects of modern life. The powerful methods and ideas developed in probability theory naturally interact with other research areas ranging from number theory to algebraic geometry within mathematics and from statistical physics to quantitative psychology outside mathematics.
The interests of faculty in the NC State Probability, Stochastic Processes and Financial Mathematics group include spectral analysis on random matrices, random signal processing, stochastic control theory, financial risk analysis, interacting particle systems, stochastic analysis and nonlinear filtering theory.
Optimal control and inverse problems for partial differential equations, control of Navier-Stokes equations, numerical partial differential equations, nonlinear semigroup theory, dynamical systems in Banach spaces, stochastic differential equations and applications, applied functional analysis.
Areas of Expertise: Analysis, Probability, Convex geometry, Discrete approximation theory, Functional inequalities.
Associate Professor, Director of Mathematics Honors Program
Probability theory and stochastic analysis, interacting particle systems, partial differential equations.
Professor, Director of Financial Mathematics Graduate Program
Stochastic control, probability, mathematical finance.
My research interests are computational finance and stochastic systems for control and optimization. Currently I am working on problems involving non-Markovian and high-dimensional optimizations. These problems were previously unsolvable due to the immensity of their computational demands. The applications of this work include financial data analysis and the challenges associate with these highly complex data sets. My background is in probability theory and nonlinear filtering. Among the newer problems that I am considering, are issues related to financial data and how machine learning methods can be applied.
Associate Professor Emeritus
Numerical analysis, financial mathematics, scientific computation, partial differential equations.
Probability theory. Main area of interest: Spectral properties of large dimensional random matrices