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I am ready for a long road flight for working with a week- or months-long projects.

December 18, 6:00 pm, R505 | Educational

Yaroslav Lyulko | Hyperplane separation theorem for Fundamental theorem of Asset Pricing.

Hyperplane separation theorem plays an importnant role in proof of Fundamental theorem of Asset Pricing (FTAP). The proof of FTAP is given at Mathematics of Finance and Valuation course however only formulation of hyperplane separation theorem is given as a reference to the fact from Linear Algebra. Due to the number of questions from students it was decided to present a complete proof of hyperplane separation theorem and link it with other fundamental results.

Upcoming plenary talks
  1. George Rafaelyan | TBA
  2. Sofya Tsay | Chi squared distribution in various topics of Statistics.
  3. Ekaterina Kupreeva | TBA
  4. Maria Nesterova | Git system: how it works and how to effectively use it.
Upcoming short talks (project / research updates)
  1. Ilya Demsky | Path-dependent Approach to Volatility: Analysis of VIX Futures Dynamics (Research update)
Educational
  1. Radon-Nikodym theorem (Gleb Pantileev).
  2. Convergence of stochastic processes (Sofya Tsay).
  3. Fourier transforms and their applications (Alexander Polyakov).
  4. Hyperplane separation theorem and its application in FTAP proof (Yaroslav Lyulko).
  5. Introduction to Optimal Stopping and Free Boundary problems (Viktoria Kurzhumova).
  6. Introduction to Machine Learning (Misha Tan).
  7. Reinforcement Learning (Luka Ilchakov).
  8. Connection between exponential distribution and setting up uniform at [0, +∞) (Polina Troshina)
  9. Glivenko-Kantelli theorem.
  10. Laplace and Esscher transforms.
  11. Kopulas method.
  12. Markov->Chebyshev->Chernov inequalities, their connections to Kullback-Leibner distance and entropy.
  13. Random forests in machine learning and connection of their loss function, complexity with enrtory.
  14. Heat equation, transfer equation and their applications.
  15. CLT for Binomial distribution. De Moivre–Laplace theorem.
  16. Kolmogorov equations via CLT. Lindeberg's condition.
  17. Monge-Kantorovich Problem.