202 Sherrerd Hall
Princeton, NJ 08544
mykhaylo at princeton.edu
I am an Associate Professor in the ORFE
Department, an Affiliated Faculty Member of the Bendheim
Center for Finance and an Associated Faculty Member with the
in Applied & Computational Math at Princeton
I was 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
My PhD is from the Math
Department at Stanford
University where my advisor
At the moment, I am
systems arising in mathematical finance, mathematical
physics, and neuroscience
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
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
Graeme Baker (expected 05/2023), Jiacheng Zhang (expected: 05/2021), Levon
Avanesyan (expected: 08/2020), Pierre
Yves Gaudreau Lamarre (defended: 05/2020), Praveen Kolli
Shkolnikov, M. (2007). Affine matrix-valued diffusions. Diploma
thesis. University of Munich.
2. Shkolnikov, M. (2009). Competing
systems evolving by i.i.d. increments. Electron.
J. Probab. 14,
3. Shkolnikov, M. (2011). Competing
systems evolving by interacting Lévy processes. Ann.
Appl. Probab. 21,
4. Shkolnikov, M. (2012). Large
of diffusions interacting through their ranks. Stoch.
Proc. Appl. 122,
5. Pal, S., Shkolnikov, M. (2014). Concentration
measure for Brownian particle systems interacting through their ranks.
Ann. Appl. Probab. 24,
6. Farinelli, S., Shkolnikov, M.
for stochastic loss given default. J.
Credit Risk 8, paper
7. Shkolnikov, M. (2013). Large
markets. Stoch. Proc. Appl.
8. Ichiba, T., Pal, S., Shkolnikov,
M. (2013). Convergence
for rank-based models with applications to portfolio theory. Probab.
Related Fields 156,
9. Karatzas, I., Shiryaev, A. N.,
Shkolnikov, M. (2011). On
the one-sided Tanaka equation with drift. Electron.
Commun. Probab. 16,
10. Ichiba, T., Karatzas, I.,
Shkolnikov, M. (2013). Strong
to stochastic equations with rank-based coefficients. Probab.
Related Fields 156,
11. Shkolnikov, M. (2011). Competing
systems and their applications. PhD
thesis, Stanford University.
12. Shkolnikov, M. (2013). Some
estimates for reversible Markov chains. Electron.
J. Probab. 18, article
13. Shkolnikov, M. (2012). On
a non-linear transformation between Brownian martingales. Submitted.
14. Gorin, V., Shkolnikov, M. (2015).
of multilevel TASEP and related processes. Ann.
Inst. Henri Poincaré Probab. Stat.
15. Gerhold, S., Kleinert, M.,
Porkert, P., Shkolnikov, M. (2015). Small
central limit theorems for semimartingales with applications. Stochastics
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.
of martingales and winning probabilities of game contestants. Electron.
J. Probab. 18, article
18. Dembo, A., Shkolnikov, M.,
Varadhan, S.R.S., Zeitouni, O. (2012). Large
deviations for diffusions interacting through their ranks. Comm.
Appl. Math. 69,
19. Racz, M.Z., Shkolnikov, M.
Brownian motions as limits of exclusion processes. Ann.
Appl. Probab. 25,
20. Ichiba, T., Shkolnikov, M.
deviations for interacting Bessel-like processes and applications to
systemic risk. Submitted.
21. Pal, S., Shkolnikov, M. (2013). Intertwining
and wave equations. Submitted.
22. Shkolnikov, M., Karatzas, I.
reflected Brownian motions in the orthant. Submitted.
23. Gorin, V., Shkolnikov, M. (2015).
Brownian motions via Jack polynomials. Probab.
Theory Related Fields 163,
24. Gorin, V., Shkolnikov, M. (2017).
systems at the edge of multilevel Dyson Brownian motions. Adv.
25. Shkolnikov, M., Sircar, R.,
Zariphopoulou, T. (2016). Asymptotic
analysis of forward performance processes in incomplete markets and
their ill-posed HJB equations. SIAM
J. Financial Math. 7,
26. Shkolnikov, M. (2015). A
construction of infinite Brownian particle systems. Submitted.
27. Gorin, V., Shkolnikov, M.
semigroup through tridiagonal matrices. Ann.
P., Shkolnikov, M. (2018). SPDE
limit of the global fluctuations in rank-based models.
K., Shkolnikov, M. (2018). Intertwinings
of beta-Dyson Brownian motions of different dimensions. Ann.
Inst. Henri Poincaré Probab. Stat.
Nadtochiy, S., Shkolnikov, M. (2019). Particle
systems with singular interaction through hitting times: application
in systemic risk modeling. Ann.
Appl. Probab. 29,
Gaudreau Lamarre, P. Y.,
Shkolnikov, M. (2019). Edge
of spiked beta ensembles, stochastic Airy semigroups and reflected
Brownian motions. Ann.
Inst. Henri Poincaré Probab. Stat. 55,
32. Almada Monter, S. A., Shkolnikov, M., Zhang, J. (2019). Dynamics
of observables in rank-based models and performance of functionally
generated portfolios. Ann.
Appl. Probab. 29,
33. Avanesyan, L., Shkolnikov, M., Sircar, R. (2018). Construction
of forward performance processes in stochastic factor models and an
extension of Widder's theorem.
To appear in Finance
34. Nadtochiy, S., Shkolnikov, M. (2018). Mean
field systems on networks, with singular interaction through hitting
times. To appear in Ann.
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. To
appear in Ann.
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, Annals of
Applied Probability meeting: Universite Nice-Sophia Antipolis, NYU,
University of Münster
2018: The 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
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
2017: London 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
2015: 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
2010: Columbia University, École d'Été de Probabilités:
Saint-Flour, EPFL Lausanne, UC Berkeley, Stanford University
A. Almada Monter, Graeme
Yves Gaudreau Lamarre, Stefan
Karatzas, Max Kleinert, Praveen
Z. Racz, Kavita