Institut für Mathematik

Prof. Dr. Ashkan Nikeghbali

Institut für Mathematik
Universität Zürich
Winterthurerstrasse 190
CH-8057 Zürich

E-Mail:
Tel.: +41 44 635 58 57
Fax: +41 44 635 57 06
Büro: Y27K10
Arbeitsfelder:
Finanzmathematik
Stochastische Prozesse
Zahlentheorie
Sekretariat:
E-Mail:
Tel.
Myriam Frank-Hilpert

+41 44 635 58 32

Events

Chair in Financial Mathematics

My research interests include:

Mathematical Finance

  • 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.

 

Other professional activity:

Since 2016 I have been a member of the Scientific Advisory Board of swissQuant and a member of the Advisory Board of EVMTech.


Vorlesungen & Seminare

Forschungsseminare
Stochastische Prozesse
Mi
17.15-19.00
Jean Bertoin, Erwin Bolthausen, Ashkan Nikeghbali, Benjamin Schlein, Alain-Sol Sznitman, Vincent Tassion, Wendelin Werner
 

Vorlesungen
(Random) Graphs with applications to risk management
Mi
10.15-12.00
Fr
10.15-12.00

Exercises (Random) Graphs with applications to risk management
Mi
13.00-14.45

Publikationen

Preprints Submitted

V. Féray, P.-L. Méliot, A. Nikeghbali
Graphons, Permutons and the Thoma simplex: three mod-Gaussian moduli spaces
Preprint (2017) PDF  

R. Chhaibi, E. Hovhannisyan, J. Najnudel, A. Nikeghbali, B. Rodgers
The limiting characteristic polynomial of classical random matrix ensembles
Preprint (2017) PDF  

M. Dal Borgo, P.-L. Méliot, A. Nikeghbali
Local Limit Theorems and mod-phi convergence
Preprint (2017) PDF  

R. Chhaibi, F. Delbaen, P.-L. Méliot, A. Nikeghbali
Mod-phi convergence, IV: Approximation of discrete measures and harmonic analysis on the torus
Preprint (2016) PDF  

V. Féray, P.-L. Méliot, A. Nikeghbali
Mod-phi Convergence, III: Multi-dimensional mod-Gaussian convergence and related estimates of probabilities
(Preliminary Version, 2015). PDF  

Published / Accepted

K. Maples, J. Najnudel, A. Nikeghbali
Limit operators for circular ensembles
To appear in Annals of Probability. PDF  

V. Féray, P.-L. Méliot, A. Nikeghbali
Mod-phi convergence, II: Estimates of the speed of convergence
To appear in Séminaire des Probabilités PDF  

R. Chhaibi, J. Najnudel, A. Nikeghbali
The Circular Unitary Ensemble and the Riemann Zeta Function: the microscopic landscape and a new approach to ratios
Invent. Math. 207, no. 1, 23--113 (2017) PDF   URL

V. Féray, P.-L. Méliot, A. Nikeghbali
Mod-phi convergence: Normality zones and precise deviations
SprigerBriefs in Probability and Mathematical Statistics PDF   URL

P.-L. Méliot, A. Nikeghbali
Mod-Gaussian convergence and its applications for models of statistical mechanics
In memoriam Marc Yor—Séminaire de Probabilités XLVII, 369--425, Lecture Notes in Math., 2137, Springer (2015). PDF   URL

E. Kowalski, J. Najnudel, A. Nikeghbali
A characterization of limiting functions arising in mod-* convergence
Electron. Commun. Probab. 20, no. 70, 1--11 (2015). PDF   URL

A. Harper, A. Nikeghbali, M. Radziwill
A note on Helson’s conjecture on moments of random multiplicative functions
Analytic Number Theory, Springer, 145--169 (2015). PDF   URL

Y. Barhoumi, C. Hughes, J. Najnudel, A. Nikeghbali
On the number of zeros of linear combinations of independent characteristic polynomials of random unitary matrices
Int. Math. Res. Not. IMRN, no. 23, 12366--12404 (2015). PDF   URL

D. Kreher, A. Nikeghbali
A new kind of augmentation of filtrations suitable for a change of probability measure by a strict local martingale
Statist. Probabilist. Lett., 104, 94--101 (2015). PDF   URL

J. Najnudel, A. Nikeghbali, A. Rouault
Limit theorems for orthogonal polynomials related to circular ensembles
J. Theoret. Probab. 29, 145--169 (2016) PDF   URL

C. Kardaras, D. Kreher, A. Nikeghbali
Strict local martingales and bubbles
Ann. Appl. Probab. 25, no.4, 1827--1867 (2015). PDF   URL

F. Delbaen, E. Kowalski, A. Nikeghbali
Mod-phi convergence
Int. Math. Res. Not. IMRN, no.11, 3445--3485 (2015). PDF   URL

J. Najnudel, A. Nikeghbali
On a flow of operators associated to virtual permutations
Séminaire de Probabilités XLVI, Lecture Notes in Math., 2123, Springer, 481--512 (2014). PDF   URL

C. Hughes, J. Najnudel, A. Nikeghbali, D. Zeindler
Random permutation matrices under the generalized Ewens measure
Annals of Applied Probability, Vol. 23(3), 987-1024 (2013) PDF   URL

A. Nikeghbali, E. Platen
A reading guide for last passage times with financial applications in view
Finance and Stochastics, Vol. 17(3), 615-640 (2013) PDF   URL

A. Nikeghbali, D. Zeindler
The generalized weighted probability measure on the symmetric group and the asymptotic behavior of the cycles
Ann. Inst. Henri Poincaré Probab. Stat. 49 (2013), no. 4, 961-981 PDF   URL

K. Maples, A. Nikeghbali, D. Zeindler
On the number of cycles in a random permutation
Electronic Communications in Probability, 17, no. 20, 1-13 (2012) PDF   URL

P. Bourgade, J. Najnudel, A. Nikeghbali
A unitary extension of virtual permutations
International Mathematics Research Notices, 2013(18):4101-4134 PDF   URL

J. Najnudel, A. Nikeghbali
The distribution of eigenvalues of randomized permutation matrices
Annales de l'institut Fourier, 63 no. 3 (2013), p. 773-838 PDF   URL

J. Najnudel, A. Nikeghbali
A new construction of the $\sigma$-finite measures associated with submartingales of class $(\Sigma)$
C. R. Math. Acad. Sci. Paris, Volume 348, pp. 311-316, (2010) PDF   URL

E. Kowalski, A. Nikeghbali
Mod-Gaussian convergence and the value distribution of zeta(1/2+it) and related quantities
Journal of the London Mathematical Society (2), 86, no. 1, 291-319 (2012) PDF   URL

A. Barbour, E. Kowalski, A. Nikeghbali
Mod-discrete expansions
Probab. Theory and Related Fields, 158, no. 3-4, 859--893 (2014). PDF   URL

J. Najnudel, A. Nikeghbali
A remarkable sigma-finite measure associated with last passage times and penalisation results
Contemporary Quantitative Finance, Essays in Honour of Eckhard Platen, pp. 77-98, Springer (2010) PDF   URL

J. Najnudel, A. Nikeghbali
On some properties of a universal sigma finite measure associated with a remarkable class of submartingales
Publ. of the Res. Instit. for Math. Sci. (Kyoto University), 47 (2011), no. 4, 911-936 PDF   URL

J. Najnudel, A. Nikeghbali
On penalization results related with a remarkable class of submartingales
Markov process. Related Fields, 19, no.4, 763--790 (2013) PDF   URL

J. Najnudel, A. Nikeghbali
A new kind of augmentation of filtrations
ESAIM, 15, pp. 39-57, (2011) PDF   URL

P. Cheridito, A. Nikeghbali, E. Platen
Processes of class sigma, last passage times, and drawdowns
SIAM Journal on Financial Mathematics, 3(2012), no. 1, 280-303 PDF   URL

J. Najnudel, A. Nikeghbali
On some universal sigma-finite measures and some extensions of Doob's optional stopping theorem
Stochastic Process. Appl., 122, no.4, 1582--1600 (2012). PDF   URL

E. Kowalski, A. Nikeghbali
Mod-Poisson convergence in probability and number theory
Intern. Math. Res. Not., 18, pp. 3549-3587, (2010). PDF   URL

J. Najnudel, A. Nikeghbali, F. Rubin
Scaled limit and rate of convergence for the largest eigenvalue from the generalized Cauchy random matrix ensemble
Journal of Statistical Physics, Volume 137, no. 2, pp. 373-406, (2009)   

J. Jacod, E. Kowalski, A. Nikeghbali
Mod-Gaussian convergence: new limit theorems in Probability and Number Theory
Forum Mathematicum, Vol. 23, No. 4, pp. 835-873, (2011) PDF   URL

D. Coculescu, M. Jeanblanc, A. Nikeghbali
Default times, non arbitrage conditions and change of probability measures
Finance and Stochastics, 16(2012), no. 3, 513-535 PDF   URL

D. Coculescu, A. Nikeghbali
Hazard processes and martingale hazard processes
Mathematical Finance 22(2012), no. 3, 519-537 PDF   URL

P. Bourgade, A. Nikeghbali, A. Rouault
Ewens measures on compact groups and hypergeometric kernels
Séminaires de Probabilités, Vol. 43, pp. 351-377, LNM 2006 (2011) PDF   URL

P. Bourgade, A. Nikeghbali, A. Rouault
Circular Jacobi ensemble and deformed Verblunsky coefficients
IMRN, Vol. 2009, No. 23, pp. 4357-4394 PDF   URL

A. Nikeghbali, M. Yor
The Barnes G function and its relations with sums and products of generalized Gamma
Elect. Comm. in Probab. 14, 396–411, (2009) PDF   URL

D. Coculescu, A. Nikeghbali
Filtrations
Encyclopedia of Quantitative Finance, Wiley, vol. II, pp. 683-686, (2010) PDF  

P. Bourgade, C. Hughes, A. Nikeghbali, M. Yor
The characteristic polynomial of a random unitary matrix: a probabilistic approach.
Duke Math. J., 145, pp. 45-69, (2008) PDF   URL

C. Hughes, A. Nikeghbali
Zeros of random polynomials cluster uniformly near the unit circle
Compositio Mathematica, vol. 144, Part 3, pp. 734-746 (2008) PDF   URL

C. Hughes, A. Nikeghbali, M. Yor
An arithmetic model for the total disorder process
Probab. Theory and Related Fields, 141, no. 1-2, pp. 47-59, (2008) PDF   URL

A. Nikeghbali
How badly are the Burholder-Davis-Gundy inequalities affected by arbitrary random times?
Statistics and Probability Letters, vol. 78, Issue 6, pp. 766-770, (2008) PDF   URL

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, pp. 229-232, (2007) PDF   URL

A. Nikeghbali
Non stopping times and stopping theorems
Stochastic Process. Appl. 117, no. 4, pp. 457-475, (2007) PDF   URL

A. Nikeghbali
Enlargements of filtrations and path decompositions at non stopping times
Probab. Theory and Related Fields, 136, no. 4, pp. 524-540, (2006) PDF   URL

A. Nikeghbali, M. Yor
Doob's maximal identity, multiplicative decompositions and enlargements of filtrations
Illinois Journal of Mathematics, 50, no. 1-4, pp. 791-814, (2006) PDF   URL

A. Nikeghbali
Multiplicative decompositions and frequency of vanishing of nonnegative submartingales
J. Theoret. Probab. 19 , no. 4, pp. 931-949, (2006) PDF   URL

A. Nikeghbali
A class of remarkable submartingales
Stochastic Process. Appli. 116, no. 6, pp. 917-938 (2006) PDF   URL

A. Nikeghbali
Some random times and martingales associated with $BES_0(\delta)$ processes ($0<\delta<2$)
ALEA Lat. Am. J. Probab. Math. Stat. 2, pp. 67-89 (2006) PDF   URL

A. Nikeghbali
An essay on the general theory of stochastic processes
Probab. Surv. 3, pp. 345-412, (2006) PDF   URL

A. Nikeghbali, M. Yor
A definition and some characteristic properties of pseudo-stopping times
Annals of Probability, Vol. 33, No. 5, pp. 1804-1824, (2005) PDF   URL

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).   

Gäste


2018201720162015201420132012201120102009Alle
GästeAufenthalt
Dr. Joseph Najnudel, School of Mathematics, University of Bristol (Bristol)
Talk: On the maximum of two log-correlated fields: the logarithms of the characteristic polynomial of the Circular Beta Ensemble and the Riemann zeta function
11.12.18 - 13.12.18Nikeghbali, Ashkan
Prof. Dr. Pierre-Loic Méliot, Département de Mathématiques, Université d'Orsay (Orsay)
28.11.18 - 05.12.18Nikeghbali, Ashkan
Dr. Oana-Valeria Stamate, Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy (Bucharest, Romania)
04.11.18 - 16.11.18Nikeghbali, Ashkan
Dr. Igor Krasovsky, Imperial College London (London)
26.09.18 - 29.09.18Nikeghbali, Ashkan
Dr. Dirk Zeindler, Lancaster University (Lancaster)
01.08.18 - 29.08.18Nikeghbali, Ashkan
Prof. Dr. Eckhard Platen, University of Technology Sydney (Sydney)
02.07.18 - 04.07.18Nikeghbali, Ashkan
Dr. Joseph Najnudel, School of Mathematics, University of Bristol (Bristol)
15.06.18 - 17.06.18Nikeghbali, Ashkan
Prof. Dr. Alain Rouault, LMV UMR, Université de Versailles-Saint-Quentin (Versailles)
15.06.18 - 16.06.18Nikeghbali, Ashkan
Prof. Dr. Pierre-Loic Méliot, Département de Mathématiques, Université d'Orsay (Orsay)
10.06.18 - 16.06.18Nikeghbali, Ashkan
Prof. Dr. Bassam Fayad, Institut de Mathématiques de Jussieu-Paris Rive Gauche (Paris)
05.04.18 - 07.04.18Nikeghbali, Ashkan
Prof. Dr. Artur Avila, Universität Zürich (Zürich)
02.04.18 - 13.04.18Nikeghbali, Ashkan
Dr. Dirk Zeindler, Lancaster University (Lancaster)
24.03.18 - 19.04.18Nikeghbali, Ashkan
Prof. Dr. Pierre-Loic Méliot, Département de Mathématiques, Université d'Orsay (Orsay)
13.03.18 - 19.03.18Nikeghbali, Ashkan
Prof. Dr. Elliot Paquette, The Ohio State University (Columbus, USA)
12.03.18 - 17.03.18Nikeghbali, Ashkan
Prof. Dr. Artur Avila, Universität Zürich (Zürich)
06.03.18 - 19.03.18Nikeghbali, Ashkan
Prof. Dr. Raphael Krikorian, Université de Cergy-Pontoise (Cergy-Pontoise, France)
06.03.18 - 10.03.18Nikeghbali, Ashkan