Mykhaylo Shkolnikov

Email:

mshkolni (at) math (dot) stanford (dot) edu

Address:

Department of Mathematics
Building 380
Stanford University
Stanford, CA 94305
USA

I'm a fifth year PhD student in the Department of Mathematics at Stanford University. My PhD advisor is Amir Dembo. Starting January 2012, I will be a postdoctoral fellow at MSRI.

My areas of research are in probability theory and mathematical finance. Currently, the focus of my research is on interacting diffusion processes and their applications in finance. I am also interested in the concentration of measure phenomenon, large deviations, random matrices and rough paths theory. 

Here you can find a list of my publications, recent talks, collaborators, and my CV



Publications:

1. Shkolnikov, M. (2007). Affine matrix-valued diffusions. Diploma thesis. University of Munich .
2. Shkolnikov, M. (2009). Competing particle systems evolving by i.i.d. increments. Electronic Journal of Probability 14 728-751. 
3. Shkolnikov, M. (2010). Competing particle systems evolving by interacting Levy processesTo appear in the Annals of Applied Probability
4. Shkolnikov, M. (2010). Large systems of diffusions interacting through their ranks. Submitted. 
5. Pal, S., Shkolnikov, M. (2010). Concentration of measure for systems of Brownian particles interacting through their ranks. Submitted. 
6. Farinelli, S., Shkolnikov, M. (2011). Two models for stochastic losses given default. Submitted. 
7. Shkolnikov, M. (2011). Large volatility-stabilized markets. Submitted. 
8. Ichiba, T., Pal, S., Shkolnikov, M. (2011). Convergence rates for rank-based models with applications to portfolio theory. Submitted.
9. Karatzas, I., Shiryaev, A. N., Shkolnikov, M. (2011). On the one-sided Tanaka equation with drift. Electronic Communications in Probability 16 664-677. 
10. Ichiba, T., Karatzas, I., Shkolnikov, M. (2011). Strong solutions to stochastic equations with rank-based coefficients. Submitted.
11. Shkolnikov, M. (2011). Competing particle systems and their applications. PhD thesis. Stanford University .
12. Dembo, A., Shkolnikov, M., Zeitouni, O. A large deviations principle for systems of diffusions interacting through their ranks. In preparation. 

Recent talks:

1. New York University, USA. September 2011.
2. Princeton University, USA. September 2011.
3. University of North Carolina/Duke University, USA. September 2011.
4. University of California, San Diego, USA. April 2011.
5. Stanford University, USA. April 2011.
6. University of Washington, Seattle, USA. March 2011.
7. Columbia University, USA. November 2010.
8. École d'Été de Probabilités, Saint-Flour, France. July 2010.
9. École Polytechnique Fédérale de Lausanne, Switzerland. June 2010.
10. University of California at Berkeley, USA. April 2010.
11. Stanford University, USA. January 2010.
12. Eidgenössische Technische Hochschule, Zürich, Switzerland. July 2009.


Collaborators:

Amir Dembo, Simone Farinelli, Tomoyuki Ichiba, Ioannis Karatzas, Soumik Pal, Albert N. Shiryaev, Ofer Zeitouni