# 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.

Kazufumi Ito

Professor

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.

Paata Ivanisvili

Assistant Professor

Areas of Expertise: Analysis, Probability, Convex geometry, Discrete approximation theory, Functional inequalities.

Min Kang

Associate Professor, Director of Mathematics Honors Program

Probability theory and stochastic analysis, interacting particle systems, partial differential equations.

Tao Pang

Professor, Director of Financial Mathematics Graduate Program

Stochastic control, probability, mathematical finance.

Andrew Papanicolaou

Assistant Professor

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.

Jeff Scroggs

Associate Professor Emeritus

Numerical analysis, financial mathematics, scientific computation, partial differential equations.

Jack Silverstein

Professor

Probability theory. Main area of interest: Spectral properties of large dimensional random matrices