## Alexander Sokol

Employment: Senior asset allocation manager at Nordea Life and Pensions
Research Interests: Statistical inference for high-dimensional data. Stochastic calculus. Causality.
E-mail: alexander.sokol@gmail.com
CV: pdf

### Math related documents:

#### Articles:

Note that the preprints on Arxiv may differ from the final published papers.
1. Sokol, Alexander, Proving existence results in martingale theory using a subsequence principle. Communications on Stochastic Analysis, Vol. 7 (2013), 65-79. Preprint
2. Sokol, Alexander, An elementary proof that the first hitting time of an open set by a jump process is a stopping time. In Séminaire de Probabilités, Vol. 45 (2013), 301-304. Preprint
3. Sokol, Alexander, Optimal Novikov-type criteria for local martingales with jumps. Electronic communications on probability, Vol. 18 (39) (2013). Preprint
4. Sokol, Alexander, An elementary proof that the first hitting time of an $F_\sigma$ set by a jump process is a stopping time. (2013). Preprint
5. Sokol, Alexander, Intervention in Ornstein-Uhlenbeck SDEs. Proceedings of the 18th EYSM (2013). Preprint
6. Sokol, Alexander & Maathuis, Marloes H. & Falkeborg, Benjamin, Quantifying identifiability in Independent Component Analysis. Electronic Journal of Statistics, Vol. 8 (2014), 1438-1459. Preprint
7. Sokol, Alexander, An extended Novikov-type criterion for local martingales with jumps. Communications on Stochastic Analysis, Vol. 8 (2014), 307-315. Preprint
8. Sokol, Alexander & Hansen, Niels R., Causal interpretation of stochastic differential equations. Electronic Journal of Probability, Vol. 19 (100) (2014). Preprint
9. Hansen, Niels R. & Sokol, Alexander, Degrees of freedom for nonlinear least squares estimation. Submitted. (2014). Preprint
10. Sokol, Alexander & Hansen, Niels R. (2012) Exponential martingales and changes of measure for point processes. Stochastic Analysis and Applications, Vol. 33, No. 5 (2015), 823-843. Preprint
11. Sokol, Alexander, A generic model for spouse's pensions with a view towards the calculation of liabilities. Insurance: Mathematics and Economics, Vol. 65 (2015), 198-207. Preprint
12. Sokol, Alexander, Revisiting the forward equations for inhomogeneous semi-Markov processes. (2015). Preprint

#### Theses and lecture notes:

Advanced probability (Lecture notes, 2013): See Lecture notes of the IMF

Stochastic integration for general semimartingales (Lecture notes, 2012): pdf

Stochastic integration for continuous semimartingales (Lecture notes, 2012): pdf

On martingales, causality, identifiability and model selection (PhD thesis, November 2013, winner of the 2014 SCIENCE prize): pdf

Stochastic Analysis and Mathematical Finance (Masters thesis, September 2008): pdf

#### Miscellaneous:

1. May 2011. Presentation on exponential martingales and construction of point processes. pdf
2. June 2011, DynStoch meeting. Poster on exponential martingales and construction of point processes. pdf
3. August 2011, ISI sattelite meeting. Presentation on estimation of sparse multivariate diffusions. pdf
4. March 2012. Presentation on exponential martingales and changes of measure. pdf
5. June 2012, DynStoch meeting. Presentation on exponential martingales and changes of measure. pdf
6. September 2012, Aarhus University. Presentation on exponential martingales and uniform integrability. pdf
7. April 2013, ETH Zurich. Presentation on SDEs as causal models. pdf
8. August 2013, 18th EYSM. Presentation on intervention in Ornstein-Uhlenbeck SDEs. pdf
9. February 2014, University of Copenhagen. PhD defense slides. pdf