In Financial Mathematics
Till August 15th (inclusive)
August 21st – 28th, 2022
Organisers cover accommodation at Kochubey Center campus, meals, as well as transfer by bus from Moscow and St. Petersburg.
departure from Moscow on August 21st at 08:00 from the MSU main building to Kochubey Center (Pushkin);
if participants reside in another city, they cover their own travel to Moscow
departure to Moscow on August 28th from Kochubey Center (Pushkin) to the MSU main building
Students in their 5th to 6th year of Specialist programs
Students in their 1st to 2nd year of Master's programs
Doctoral students
in the following fields:
Mathematics and related fields,
Information Technology and related fields,
Economic fields with advanced mathematics
Kochubey Center, town of Pushkin (St. Petersburg)
Till August 17th
AUGUST 21st – 28th
Advanced-level week-long workshop on modern financial mathematics by recognized international and Russian experts.
Organisational Committee
Yuri Kabanov
Committee chairman, Dr. of Phys. and Maths, Professor at Moscow School of Economics, Faculty of Mechanics and Mathematics, Moscow State University
Kirill Klimov
Cand. Sci. in Phys. and Maths, CEO, Member of the Board of Directors at the Vega Institute Foundation
Marianna Tsareva
Deputy Chief Executive Officer at the Vega Institute Foundation
Valeria Stefanenko
Head of Development at the Vega Institute Foundation
Valeria Volobueva
Project Manager of Educational Initiatives at the Vega Institute Foundation
Member of the Russian Academy of Sciences, Dr. of Phys. and Maths, Honored Professor at Lomonosov Moscow State University, Head of the Department of Probability Theory
Special guest
Albert Shiryaev
Brownian motion and Wiener measure
Miryana Grigorova
Non-linear Dynkin games with applications to pricing, hedging and risk management
University of Warwick

This series of lectures will explore the topic of (two-player) Dynkin games (or games on stopping times) and some extensions thereof, their connections with Reflected Backward Stochastic Equations with two reflecting obstacles, as well as some financial applications.

The tentative programme of the course includes:
linear and non-linear Dynkin games of zero-sum type in discrete time (which will allow us to fix/recall some notions); Nash equilibrium in a (linear and non-linear) Dynkin game of non-zero-sum type in discrete time; linear and non-linear Dynkin games in continuous time (and some extensions thereof) and their connections with Reflected Backward Stochastic Equations with two reflecting obstacles; applications to pricing and hedging of game options in complete market models; linear and non-linear games in incomplete market models, games of control and stopping which appear naturally in such frameworks,…

Mikhail Zhitlukhin
Fast computations in Python with application in financial mathematics
Steklov Mathematical Institute of the Russian Academy of Sciences
In this course, we will cover the Python tools that allow for significantly faster and more efficient calculations. We will begin with the well-known NumPy package, which implements fast array operations.
Then we will discuss the Numba package, which allows for just-in-time compilation of Python code and easy parallel computation on multiple CPU cores.
In the third part of the course, we will examine methods for implementing computations on graphics processors using the CuPy package.

To demonstrate the application examples for these packages, we will analyze the task of implementing the Monte Carlo method in the Heston model and the task of fitting the parameters of the Heston model to observed European option prices.
Vassili Kolokoltsov
Introduction to the duality of Markov processes with applications in finance and actuarial science
Professor at Lomonosov Moscow State University, Professor Emeritus of University of Warwick

We shall present a unifying theory of the duality of Markov processes that encompasses in particular the notion used in insurance mathematics (sometimes referred to as Siegmund's duality) for the study of ruin probability and the duality responsible for the so-called put - call symmetries in option pricing. Other applications of duality arise in theory of interacting particles, in the theory of super-processes and in the models of evolutionary biology (Fisher diffusion).

Our general kth order duality can be financially interpreted as put - call symmetry for powered options. We shall develop an effective analytic approach to the analysis of duality leading to the full characterization of kth order duality of Markov processes in terms of their generators.

Stanislav Shaposhnikov
Superposition principle for probabilistic solutions of the Fokker-Planck-Kolmogorov equation
Lomonosov Moscow State University

The Fokker-Planck-Kolmogorov equation appears in various economic, sociological, biological, and physical models that use diffusion processes for their construction. The superposition principle expresses a deep connection between probabilistic solutions of the Fokker-Planck-Kolmogorov equation and solutions of the corresponding martingale problem, and has been actively studied in recent years, with the most well-known results obtained in the works of L. Ambrosio, A. Figalli, and D. Trevisan.

Currently, the superposition principle is actively used to prove the existence and uniqueness of probabilistic solutions, to obtain probabilistic representations of solutions to nonlinear equations, and to investigate mean-field game problems.

In this course, the basis for the superposition principle will be given, along with its generalizations and applications. In addition, several open problems related to the superposition principle and the Fokker-Planck-Kolmogorov equation will be discussed.

Selection of participants is competitive and based on expert evaluation of the following portfolio positions:
How to join
Participating in each of the academic and extracurricular events at the Summer School is compulsory.
Participant may be individually exempt from an event based on a valid reason presented to the organisers.

The Foundation reserves the right to expel participants for violating the regulations.
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