Prof. Dr. Ashkan Nikeghbali
Chair in Financial Mathematics
My research interests include:
- Loss portfolios, modeling dependence;
- Applications of the theory of enlargements of filtrations and random times to mathematical finance.
Random matrix theory
- Study of the classical groups, eigenvalues asymptotics, distribution of the characteristic polynomial and ratios;
- Orthogonal polynomials on the unit circle;
- Random operators associated to random matrices.
Mod-phi convergence and limit theorems for dependent random variables
- Weak convergence, distributional approximations, rate of convergence;
- Normality zones;
- Precise moderate and large deviations;
- Applications to combinatorics, random graphs, random permutations, statistical mechanics, sums of weakly dependent random variables, random matrix theory, mathematical finance.
Analytic number theory
- Distribution of values of L-functions, density problems, limit theorems for L-functions, random matrix models and prediction in number theory;
- Random multiplicative functions.