Ashkan Nikeghbali

Ashkan Nikeghbali Professor Institute of Mathematics University of Zürich Office: Y27J22 Campus Zürich-Irchel Address: Winterthurerstr. 190 CH-8057 Zürich Tel: +41-(0)44-63 55857. Fax: +41-(0)44-63 55706 e-mail: ashkan dot nikeghbali at math dot uzh dot ch

Research	Publications	Selected Talks	Brief Professional Bio	Teaching	News

Research	Random matrix theory: study of the classical groups, distribution of the characteristic polynomial, orthogonal polynomial on the unit circle. The theory of stochastic processes: fine properties of martingales and diffusions, enlargements of filtrations, Brownian Motion, random times, limit theorems. Analytic number theory: distribution of values of L-functions, density problems, limit theorems for L-functions, random matrix models and prediction in number theory, equidistribution problems, zeros of (random) polynomials. Mathematical finance: applications of the theory of enlargements of filtrations and random times to mathematical finance, models of default risk, insider trading models.
Publications	J. Najnudel, A. Nikeghbali A new construction of the $\sigma$-finite measures associated with submartingales of class $(\Sigma)$ Preprint (2009). PDF E. Kowalski, A. Nikeghbali Mod-Gaussian convergence and the value distributions of $\zeta(1/2+it)$ and related quantities Preprint (2009). PDF A.D. Barbour, E. Kowalski, A. Nikeghbali Mod-discrete expansions Preprint (2009). PDF J. Najnudel, A. Nikeghbali A remarkable sigma-finite measure associated with last passage times and penalisation problems Preprint (2009). PDF J. Najnudel, A. Nikeghbali On penalisation results related with a remarkable class of submartingales Preprint (2009). PDF J. Najnudel, A. Nikeghbali On some properties of a universal sigma-finite measure associated with a remarkable class of submartingales Preprint (2009). PDF P. Cheridito, A. Nikeghbali, E. Platen Processes of class Sigma, last passage times and drawdowns Preprint (2009). PDF J. Najnudel, A. Nikeghbali A new kind of augmentation of filtrations Preprint (2009). PDF J. Najnudel, A. Nikeghbali On some universal sigma finite measures and some extensions of Doob's optional stopping theorem Preprint (2009). PDF E. Kowalski, A. Nikeghbali Mod-Poisson convergence in probability and number theory Preprint (2009). PDF J. Najnudel, A. Nikeghbali, F. Rubin Scaled limit and rate of convergence for the largest eigenvalue from the generalized Cauchy random matrix ensemble. To appear in Journal of Statistical Physics. PDF D. Coculescu, M. Jeanblanc, A. Nikeghbali Default times, non arbitrage and change of probability measures. Preprint (2008). PDF P. Bourgade, A. Nikeghbali, A. Rouault Circular Jacobi ensemble and deformed Verblunsky coefficients To appear in IMRN. PDF J. Jacod, E. Kowalski, A. Nikeghbali Mod-Gaussian convergence: new limit theorems in Probability and Number Theory To appear in Forum Mathematicum. PDF A. Nikeghbali, E. Platen On honest times in financial modeling. Preprint (2008). PDF D. Coculescu, A. Nikeghbali Hazard Processes and martingale hazard processes. Preprint (2008). PDF A. Nikeghbali A generalization of Doob's maximal identity. Preprint (2008). PDF P. Bourgade, A. Nikeghbali, A. Rouault Hua-Pickrell measures on general compact groups. Preprint (2007). PDF A. Nikeghbali, M. Yor The Barnes G function and its relations with sums and products of generalized Gamma convolutions. Elect. Comm. in Probab. 14 (2009), 396–411. PDF D. Coculescu, A. Nikeghbali Filtrations. To appear in Encyclopedia of quantitative finance, Wiley (2007). PDF P. Bourgade, C. Hughes, A. Nikeghbali, M. Yor The characteristic polynomial of a random unitary matrix: a probabilistic approach. Duke Math. J., 145, 45--69 (2008). PDF C. Hughes, A. Nikeghbali The zeros of characteristic polynomials cluster uniformly near the unit circle. Compositio Mathematica, vol. 144, Part 3, 734-746 (2008). PDF C. Hughes, A. Nikeghbali, M. Yor An arithmetic model for the total disorder process. Probab. Theory and Related Fields, 141, no. 1-2, 47-59 (2008). PDF A. Nikeghbali How badly are the BDG inequalities affected by arbitrary random times? Statistics and Probability Letters, vol. 78, Issue 6, p.766-770 (2008). PDF P. Bourgade, A. Nikeghbali, A. Rouault The characteristic polynomial on compact groups with Haar measure: some equalities in law. C. R. Acad. Sci. Paris, Ser. I, 345, no.4, 229-232 (2007). PDF A. Nikeghbali Non stopping times and stopping theorems. Stochastic Process. Appl. 117, no.4, 457-475 (2007). PDF A. Nikeghbali Enlargements of filtrations and path decompositions at non stopping times. Probab. Theory and Related Fields, 136, no. 4, 524-540 (2006). PDF A. Nikeghbali, M. Yor Doob's maximal identity, multiplicative decompositions and enlarge- ments of filtrations. Illinois Journal of Mathematics, 50, no. 1-4, 791-814 (2006). PDF A. Nikeghbali Multiplicative decompositions and frequency of vanishing of nonnegative submartingales. J. Theoret. Probab. 19 , no. 4, 931-949 (2006). PDF A. Nikeghbali A class of remarkable submartingales. Stochastic Process. Appli. 116, no. 6, 917-938 (2006). PDF A. Nikeghbali Some random times and martingales associated with $BES_0(\delta)$ processes ($0<\delta<2$). ALEA Lat. Am. J. Probab. Math. Stat. 2, 67-89 (2006). PDF A. Nikeghbali An essay on the general theory of stochastic processes. Probab. Surv. 3, 345-412 (2006). PDF A. Nikeghbali, M. Yor A definition and some characteristic properties of pseudo-stopping times. Annals of Probability, Vol. 33, No. 5, 1804-1824 (2005). PDF A. Nikeghbali "Temps aleatoires, filtrations, sous-martingales: quelques developpements recents." Ph.D in mathematics supervised by Marc Yor: Universite Pierre et Marie Curie, Paris 6 (2005).
Selected Talks	Quantitative Methods in Finance, Sydney, December 2009, invited plenary speaker. Workshop on mathematical finance and related topics in economics and engineering, Kyoto, August 2009. Stochastic Analysis For and From Finance, Conference, Kyoto, August 2009. Stochastic Processes and their Applications, August 2009, invited speaker. Istanbul worlkshop on mathematical finance, May 2009. Colloquium, Princeton University, ORFE, March 2009. Workshop on probability and statistical mechanics, Neuchatel, September 2008. Mathematical physics winter meeting, ETHZ, September 2008. Seminaire de probabilites, Ecole Normale Superieure de Lyon, June 2008. Probability seminar, Oxford University, May 2008. Colloquium, Princeton University, ORFE, May 2008. Financial Engineering Seminar, Cornell University, May 2008. Stochastic Analysis Seminar, Princeton University, May 2008. Random Matrix Theory: probabilistic aspects, Hausdor Institute, Bonn, Jan 2008. Inaugural Lecture, University of Zürich, December 2007. Number theory and Random Phenomena, Bristol, UK, March 2007. Advanced Mathematical Models for Finance, Toulouse, January 2007. Swiss Probability Seminar, Bern, June 2006. Phenomena in high dimensions, Institut Henri Poincare, May 2006. Probability Seminar, Stanford University, April 2006. Probability Seminar, Berkeley University, March 2006. Symposium in applied mathematics, University of Zürich, February 2006. CIRM (Centre International de Recherches Math ematiques), Luminy, Journees de probabilites, September 2004. Isaac Newton Institute, Matrix Ensembles and L-Functions, July 2004.
Brief Professional Bio	Heinz Hopf Lecturer, ETH Zürich, June 2006-March 2007. Postdoc, American Institute of Mathematics and Rochester University, May 2005-June 2006. Ph.D. in Mathematics, Universite Pierre et Marie Curie, Paris 6, September 2005. Thesis "Temps al eatoires, ltrations, sous martingales: quelques d eveloppements r ecents" supervised by Marc Yor.
Teaching	Applied Mathematics, University of Zürich, SS 2009. Introduction to Mathematical Finance, University of Zürich, 2008/2009. Advanced undergraduate course in analytic number theory, University of Zürich, 2007/2008. Graduate course on Brownian Motion and stochastic calculus, University of Zürich, 2007. Student Seminar on Stochastic Calculus, University of Zürich, 2007 Graduate course on the random matrix approach in number theory, ETH Zürich, 2006.
News	From October 27 to October 31 (2008), Emmanuel Kowalski and myself organized the conference "Random Matrices, L- Functions and Primes" at ETH Zürich, sponsored by the Forschungsinstitut für Mathematik.