Prof. Dr. Ashkan Nikeghbali
Universität Zürich
Winterthurerstrasse 190
CH-8057 Zürich
E-Mail:
Fax: +41 44 635 57 06
Büro: Y27K10
Stochastische Prozesse
Zahlentheorie
E-Mail:
Tel.:
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:
I am a strategy advisor at Roche for stochastic modeling and data analytics, from October 2020.
Since 2016 I have been a member of the Scientific Advisory Board of swissQuant and a member of the Advisory Board of EVMTech.
I was awarded an Honorary Doctorate from the "1 Decembrie 1918" University of Alba Iulia.
Publikationen
Preprints SubmittedP.-L. Méliot, A. Nikeghbali, G. Visentin
Mod-Poisson approximation schemes: applications to credit risk
Preprint PDF
P.-L. Méliot, A. Nikeghbali, G. Visentin
Mod-Poisson approximation schemes and higher order Chen-Stein inequalities
Preprint PDF
P.-L. Méliot, A. Nikeghbali
Asymptotics of the major index of a random standard tableau
Preprint PDF
P.-L. Méliot, A. Nikeghbali
Gaussian approximations for random vectors
Preprint. PDF
G. Genovese, A. Nikeghbali, N. Serra, G. Visentin
Universal approximation of credit portfolio using restricted Boltzmann machines
Preprint. PDF
P.-L. Méliot, A. Nikeghbali
On the precise deviations of the characteristic polynomial of a random matrix
Preprint. PDF
J. Najnudel, A. Nikeghbali
Convergence of random holomorphic functions with real zeros and extensions of the stochastic zeta function
Preprint. PDF
V. Féray, P.-L. Méliot, A. Nikeghbali
Graphons, Permutons and the Thoma simplex: three mod-Gaussian moduli spaces
To appear in the Proceedings of the London Mathematical Society. PDF
R. Chhaibi, F. Delbaen, P.-L. Méliot, A. Nikeghbali
Mod-phi convergence, IV: Approximation of discrete measures and harmonic analysis on the torus
To appear in Annales de l'Institut Fourier PDF
R. Chhaibi, E. Hovhannisyan, J. Najnudel, A. Nikeghbali, B. Rodgers
The limiting characteristic polynomial of classical random matrix ensembles
To appear In Annales de l'IHP. PDF
M. Dal Borgo, P.-L. Méliot, A. Nikeghbali
Local Limit Theorems and mod-phi convergence
To appear in ALEA. PDF
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
2024 | 2023 | 2022 | 2021 | 2020 | 2019 | 2018 | 2017 | 2016 | 2015 | Alle |
Gäste | Aufenthalt | |
Prof. Dr. Joseph Najnudel, University of Bristol (Bristol, UK) Talk: Loss surfaces of neural networks and random matrix theory | 18.09.23 - 22.09.23 | Nikeghbali, Ashkan |
Dr. Ionel Popescu, Institute of Mathematics of the Romanian Academy IMAR (Bucharest, Romania) | 03.09.23 - 06.09.23 | Nikeghbali, Ashkan |
Dr. Reda Chhaibi, Université Paul Sabatier (Toulouse) | 11.04.23 - 13.04.23 | Nikeghbali, Ashkan |
Prof. Dr. Joseph Najnudel, University of Bristol (Bristol, UK) | 10.04.23 - 14.04.23 | Nikeghbali, Ashkan |
Anlässe
The Secret of Life Research Camp
November 22 - 26, 2021, in Zurich
8th Strasbourg / Zurich - Meeting: Frontiers in Analysis and Probability
November 28 - 29, 2019, in Zurich
7th Strasbourg / Zurich - Meeting: Frontiers in Analysis and Probability
October 25 - 26, 2018, in Strasbourg
Random geometries / Random topologies
December 4 - 5, 2017, at ETH Zürich, in Zurich
6th Strasbourg / Zurich - Meeting: Frontiers in Analysis and Probability
October 31 - November 1, 2017, in Zurich
5th Strasbourg / Zurich - Meeting: Frontiers in Analysis and Probability
March 23 - 24, 2017, in Strasbourg
4th Strasbourg / Zurich - Meeting: Frontiers in Analysis and Probability
November 3 - 4, 2016, in Zurich
Enlargements of Filtrations and Financial Applications
May 2 - 3, 2016, in Évry
September 8 - 9, 2016, in Zurich
50th Swiss Probability Seminar
June 6 - 7, 2016, in Zurich
3rd Strasbourg / Zurich - Meeting: Frontiers in Analysis and Probability
March 4 - 5, 2016, in Strasbourg
2nd Strasbourg / Zurich - Meeting: Frontiers in Analysis and Probability
October 29 - 30, 2015, in Zurich
1st Strasbourg / Zurich - Meeting: Frontiers in Analysis and Probability, February 19 - 20, 2015, in Strasbourg
Swiss Probability Seminar
Workshop on Mathematics in Finance, October 18, 2013
Workshop on Lévy processes and their applications, December 13 - 14, 2010
Workshop on Random Matrices, April 15 - 16, 2010
From October 27 - 31, 2008, Emmanuel Kowalski and myself organized the conference
"Random Matrices, L- Functions and Primes" at ETH Zürich,
sponsored by the Forschungsinstitut für Mathematik