202 Sherrerd Hall
Princeton, NJ 08544
Currently, I am an
Assistant Professor in the ORFE Department, an Affiliated Faculty Member of the Bendheim Center for Finance and an Associated Faculty Member with the Program in Applied & Computational Math at
University, after being an Assistant Professor in the Math
Department at Princeton. Before coming to Princeton I was a
Postdoctoral Fellow at UC
Berkeley and MSRI
mentored by David Aldous. My PhD is from the Math Department at Stanford University
where my advisor was Amir Dembo.
At the moment, I am studying interacting
particle systems arising in mathematical finance, mathematical physics, and neuroscience using tools from stochastic analysis and PDE/SPDE. More broadly, my interests include a
variety of topics in probability theory and PDEs: random operators, integrable probability, models of random growth, concentration of measure, large deviations,
and probabilistic approaches to hyperbolic and parabolic PDEs.
My research is partially supported by the NSF grant DMS-1811723 and a Princeton SEAS innovation award.
Here you can find activities I am involved
in, my PhD students, publications, talks, collaborators, and CV.
Jiacheng Zhang (expected: 05/2021), Pierre Yves
Lamarre (expected: 05/2020), Levon Avanesyan (expected: 05/2020), Praveen Kolli (defended: 04/2018)
matrix-valued diffusions. Diploma
thesis. University of Munich.
2. Shkolnikov, M. (2009).
particle systems evolving by i.i.d. increments. Electron. J. Probab. 14, 728-751.
3. Shkolnikov, M. (2011).
particle systems evolving by interacting Lévy processes. Ann. Appl. Probab. 21, 1911-1932.
4. Shkolnikov, M. (2012). Large
systems of diffusions interacting through their ranks. Stoch. Proc. Appl. 122, 1730-1747.
5. Pal, S., Shkolnikov, M. (2014).
of measure for Brownian particle systems interacting
through their ranks. Ann. Appl.
Probab. 24, 1482-1508
6. Farinelli, S., Shkolnikov, M.
models for stochastic loss given default. J. Credit Risk 8, paper 4.
7. Shkolnikov, M. (2013). Large
volatility-stabilized markets. Stoch.
Proc. Appl. 123,
8. Ichiba, T., Pal, S.,
Shkolnikov, M. (2013). Convergence
rates for rank-based models with
applications to portfolio theory. Probab.
9. Karatzas, I., Shiryaev, A. N.,
Shkolnikov, M. (2011). On the one-sided Tanaka
equation with drift.
Electron. Commun. Probab.
10. Ichiba, T., Karatzas, I.,
Shkolnikov, M. (2013). Strong
solutions to stochastic equations with
rank-based coefficients. Probab.
Theory Related Fields 156,
11. Shkolnikov, M. (2011).
particle systems and their applications. PhD thesis, Stanford University.
12. Shkolnikov, M. (2013). Some
universal estimates for reversible Markov chains. Electron. J. Probab. 18, article 11.
13. Shkolnikov, M. (2012). On a
non-linear transformation between Brownian martingales. Submitted.
14. Gorin, V., Shkolnikov, M.
(2015). Limits of
multilevel TASEP and related processes. Ann. Inst. Henri Poincaré Probab. Stat. 51, 18-27.
15. Gerhold, S., Kleinert, M.,
Porkert, P., Shkolnikov, M. (2015). Small
time central limit theorems
for semimartingales with applications. Stochastics 87, 723-746.
16. Karatzas, I., Pal, S.,
Shkolnikov, M. (2016). Systems of
Brownian particles with asymmetric
collisions. Ann. Inst. Henri
Poincaré Probab. Stat. 52,
17. Aldous, D., Shkolnikov, M.
(2013). Fluctuations of
martingales and winning probabilities of game
contestants. Electron. J. Probab.
18, article 47.
18. Dembo, A., Shkolnikov, M.,
Varadhan, S.R.S., Zeitouni, O. (2012). Large deviations for diffusions
interacting through their ranks. Comm.
Pure Appl. Math. 69,
19. Racz, M.Z., Shkolnikov, M.
sticky Brownian motions as limits of exclusion
processes. Ann. Appl. Probab.
20. Ichiba, T., Shkolnikov, M.
deviations for interacting Bessel-like processes and
applications to systemic risk. Submitted.
21. Pal, S., Shkolnikov, M.
diffusions and wave equations. Submitted.
22. Shkolnikov, M., Karatzas, I.
of reflected Brownian motions in the orthant. Submitted.
23. Gorin, V., Shkolnikov, M.
Dyson Brownian motions via Jack polynomials. Probab. Theory Related Fields 163, 413-463.
24. Gorin, V., Shkolnikov, M.
particle systems at the edge of multilevel Dyson
Brownian motions. Adv. Math. 304, 90-130.
25. Shkolnikov, M., Sircar, R.,
Zariphopoulou, T. (2016). Asymptotic analysis of forward performance processes
markets and their ill-posed HJB equations. SIAM J. Financial Math. 7, 588-618.
26. Shkolnikov, M. (2015). A
construction of infinite Brownian particle systems. Submitted.
27. Gorin, V., Shkolnikov, M.
Airy semigroup through tridiagonal matrices. Ann. Probab. 46, 2287-2344.
. Kolli, P., Shkolnikov, M.
(2018). SPDE limit of
the global fluctuations in rank-based models. Ann. Probab. 46, 1042-1069.
. Ramanan, K., Shkolnikov, M.
(2018). Intertwinings of beta-Dyson Brownian motions of different dimensions. Ann. Inst. Henri
Poincaré Probab. Stat. 54, 1152-1163.
. Nadtochiy, S., Shkolnikov, M. (2019). Particle systems with singular interaction through hitting times: application in systemic risk modeling. Ann. Appl. Probab. 29, 89-129.
. Gaudreau Lamarre, P. Y., Shkolnikov, M. (2017). Edge of spiked beta ensembles, stochastic Airy semigroups and reflected Brownian motions. To appear in Ann. Inst. Henri
Poincaré Probab. Stat.
32. Almada Monter, S. A., Shkolnikov, M., Zhang, J. (2018). Dynamics of observables in rank-based models and performance of functionally generated portfolios. To appear in Ann. Appl. Probab.
33. Avanesyan, L., Shkolnikov, M., Sircar, R. (2018). Construction of forward performance processes in stochastic factor models and an extension of Widder's theorem. Submitted.
34. Nadtochiy, S., Shkolnikov, M. (2018). Mean field systems on networks, with singular interaction through hitting times. Submitted.
35. Delarue, F., Nadtochiy, S., Shkolnikov, M. (2019). Global solutions to the supercooled Stefan problem with blow-ups: regularity and uniqueness. Submitted.
36. Lacker, D., Shkolnikov, M., Zhang, J. (2019). Inverting the Markovian projection, with an application to local stochastic volatility models. Submitted.
Vienna, London School of Economics, Imperial College London, Rutgers
University, 4th Berlin-Princeton-Singapore Workshop on Quantitative
Finance: National University of Singapore, MIT, Centre International de
Recontres Mathematiques (Luminy): Integrability and Randomness in
Mathematical Physics and Geometry, Southeastern Probability Conference:
Duke University, SIAM Conference on Financial Mathematics &
Engineering: Toronto, Berlin Mathematical Finance Seminar, NYU, INFORMS
Annual Meeting: Seattle
Hong Kong Polytechnic University, University of Toronto, Columbia University, Duke University, Seminar on
Stochastic Processes: Brown University, Casa Mathemática Oaxaca:
Workshop on Stochastic Analysis and its Applications, Institut
Mittag-Leffler: Gaussian fields in random matrix theory,
Illinois Institute of Technology, AMS sectional meeting: University of
Delaware, Program in Applied & Compuational Mathematics colloquium:
Princeton University, Eastern Conference on Mathematical Finance:
Illinois Institute of Technology, Advances in Asymptotic Probability
(in honor of Amir Dembo's 60th birthday): Stanford University, TU Munich
Mathematical Finance Seminar, Columbia University, Oberwolfach:
Mathematics of Quantitative Finance, Western Conference in
Mathematical Finance, University of Michigan, Oxford University:
Oxford-Princeton Workshop on Financial Mathematics & Stochastic
Analysis, Edinburgh: Workshop on BSDEs, SPDEs and their Applications,
Montreal: Mathematical Congress of the Americas (Probability Theory
session), SIAM-LMS Conference on Mathematical Modelling in Finance, Stony Brook, University of Vienna, UT Austin
2016: Kavli Institute for Theoretical
Physics: Non-equilibrium dynamics of stochastic and quantum integrable
systems, UC Santa Barbara,
Rutgers University, MIT,
University of Michigan: Byrne Workshop in Stochastic Analysis in
Finance and Insurance, International Centre for Mathematical Sciences,
Edinburgh: At the Frontiers of Quantitative Finance
Canadian Mathematical Society conference: Montréal, University of
Chicago, Northeast Probability Seminar: NYU, 9th Oxford-Princeton
Workshop on Financial Mathematics and Stochastic Analysis, Morgan
Stanley, TU Munich, University of Tokyo, Stochastic Portfolio Theory
conference: Columbia University, Mathematical Finance and Partial
Differential Equations conference: Rutgers University, CUNY, AMS
sectional meeting: DC, Rutgers University, Princeton University
2014: Brown University, University
of Tokyo, Johns Hopkins, Harvard University, University of
Pennsylvania/Temple University, Princeton University, University of
Connecticut, Columbia University, University of Southern California,
University of British Columbia, University of Maryland, Georgia Tech
2013: University of Bonn,
University of Minnesota, Carnegie Mellon University, Cornell
University, Conference on Stochastic Processes and Their Applications
(SPA): University of Colorado, Stanford University, University of
Michigan, Columbia University, MIT, University of Washington, UC
Berkeley, AMS meetings: San Diego
2012: UC Santa Barbara, Conference
in honor of Ioannis Karatzas: Columbia University, Mathematical
Sciences Research Institute, UC Berkeley, MAN Institute at Oxford
University, ETH Zurich, University of Technology Vienna
2011: QMF 2011 conference: Sydney,
UCLA, UC Irvine, UC Berkeley, New York University, Princeton
University, University of North Carolina/Duke University, UC San Diego,
Stanford University, University of Washington
2010: Columbia University, École d'Été de Probabilités:
Saint-Flour, EPFL Lausanne, UC Berkeley, Stanford University
, David Aldous, Sergio A. Almada Monter, Francois Delarue, Amir
Farinelli, Pierre Yves Gaudreau Lamarre, Stefan Gerhold, Vadim Gorin,
Karatzas, Max Kleinert, Praveen
Kolli, Daniel Lacker, Sergey Nadtochiy, Soumik Pal, Piet
Porkert, Miklos Z.
Racz, Kavita Ramanan,
N. Shiryaev, Ronnie Sircar, S.R.Srinivasa
Zariphopoulou, Ofer Zeitouni
, Jiacheng Zhang