Joint Seminar of the Department of Probability Theory & Vega Foundation
The speakers of the seminar introduce the listeners to the latest achievements in the field of financial and actuarial mathematics.
The seminar is primarily aimed at undergraduate students of last two years, graduate students and PhD students. However, everyone can take part, having passed the preliminary registration.
The leaders of the seminar are Academician of the Russian Academy of Sciences Albert Nikolaevich Shiryaev, Chief Executive Officer of the Foundation Kirill Yuryevich Klimov and Senior Researcher of the Steklov Mathematical Institute of Russian Academy of Sciences Mikhail Valentinovich Zhitlukhin
Teachers
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Language: Russian, English
Format: online
SCHEDULE FOR THE SPRING SEMESTER' 23
March 01, 18:30-20:00
Vsevolod ZAOSTROVSKII
Scientific supervisor: Yury Mikhailovich Kabanov
Local and stochastic volatility models
Ivan CHEREPAKHIN
Scientific supervisor: Yury Mikhailovich Kabanov
Breakdown of the Wiener process using wavelet
Diana KALIKAEVNA
Scientific supervisor: Alexander Yurievich Veretennikov
Recursive properties of "Markov-up" processes
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March 15, 18:30-20:00
Askhab SULEYMANOV
Scientific supervisor: Elena Evgenievna Bashtova
The probability of non-ruin by the t-time in the insurance model with capital investment
Anastasia MAKHOVA
Scientific supervisor: Mikhail Ivanovich Kumskov
Forecasting financial time-series using neural networks with memory
Vladislav ZYUZIN
Scientific supervisor: Mikhail Ivanovich Kumskov
Forecasting financial time-series
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March 22, 18:30-20:00
Makar PRIKHODKO
Scientific supervisor: Ekaterina Vadimovna Bulinskaya
Analysis of methods for calculating insurance premiums
Andrey KANAEV
Scientific supervisor: Elena Borisovna Yarovaya
Application of branching processes in financial mathematics
Danila SHABALIN
Scientific supervisor: Ekaterina Vadimovna Bulinskaya
Research of ruin probability for some insurance models
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March 29, 18:30-20:00
Alexander RAKITKO
Graduate of the Faculty of Mechanics and Mathematics of Lomonosov Moscow State University, medical genetic center Genotek
Scientific supervisor: A. Bulinsky
Identification of significant collections of factors with error functional estimation
The problem of multifactorial dimensionality reduction (MDR) arises naturally in different applications. We consider MDR-EFE (error function estimation) method for the identification of significant collections of factors. The asymptotic results (criterion of almost sure convergence, several variants of central limit theorems and others) are proven using the martingale technique, theory of exchangeable variables for various modifications of MDR-EFE method. Theoretical results are supported by computer simulations.
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April 5, 18:30-20:00
Ivan POLOZOV
Scientific supervisor: TBC
To be confirmed
Ruslan GURIEV
Scientific supervisor: Ekaterina Mikhailovna Ryadnova
Extrema of random networks and their connection with p2p-exchanges
Valentin KUZMENKO
Scientific supervisor: Ekaterina Mikhailovna Ryadnova
Analysis of financial data with an index of extreme values close to 0
Tigran MATEVOSYAN
Scientific supervisor: Aleksandr Aleksandrovich Gushchin
Martingale cuplings
Gordey VERBIY
Scientific supervisor: Maksim Petrovich Zapletin
Stochastic optimization of portfolio investments
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April 12, 18:30-20:00
Dmitry ROKHLIN
Professor of the Department of Higher Mathematics and Operations Research, Southern Federal University
Online optimization and some applications
Methods of convex online optimization allows for construction of theoretically grounded recurrent algorithms for solving optimization problems involving unknown varying factors. The principles for constructing such algorithms will be discussed as well as a number of applications: dynamic portfolio problem, the problem of finding incentive prices and regression problem with random features.
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April 19, 18:30-20:00
TBA
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April 26, 18:30-20:00
Rustam IBRAGIMOV
Professor of Finance and Econometrics at Imperial College Business School, London, UK
TBA
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SCHEDULE FOR THE FALL SEMESTER'22
October 19, 18:10-19:30
Albert Nikolaevich SHIRYAEV ,
Academician of the Russian Academy of Sciences, Doctor of Physical and Mathematical Sciences, Head of the Department of Probability Theory
Randomness in probability
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October 26, 18:10-19:30
Ivan Valerievich OSELEDETS ,
Doctor of Physical and Mathematical Sciences, Professor of the Russian Academy of Sciences, Director of the Skoltech AI Technology Center, Leading Researcher, Institute of Computational Mathematics of the Russian Academy of Sciences and AIRI
Methods of tensor expansions and their applications
The lecture will give an overview of basic approaches for efficient representations of multidimensional arrays and some applications of such approaches.
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November 02, 18:10-19:30
Vladimir Vladimirovich PITERBARG ,
PhD, Global Head Of Quantitative Analytics, NatWest Markets
Alternatives to Deep Neural Networks for Function Approximations in Finance: Function Fitting and Regressions
We develop two methods for approximating slow-to-calculate functions, and for conditional expected value calculations: the generalized stochastic sampling (gSS) and the functional tensor train (fTT) methods. We propose them as highly-performing alternatives to generic deep neural networks (DNNs) currently routinely recommended in derivatives pricing and other quantitative finance applications. The new methods not only outperform DNNs for typical financial problems but also, unlike DNNs, satisfy stringent finance requirements such as predictability and explainability.WATCH IT IN THE RECORDING
November 09, 18:10-19:30
Platon Valerievich PROMYSLOV ,
Doctoral student of the Department of Probability Theory, Faculty of Mechanics and Mathematics, Moscow State University
Sparre Andersen's Bankruptcy Models with Investments
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November 16, 18:10-19:30
Anna Alexandrovna OBIZHAEVA ,
Ph.D., MIT Sloan, Professor, Director of the NES Master of Finance program
Dimensional Analysis, Leverage Neutrality, and Market Microstructure Invariance
This paper combines dimensional analysis, leverage neutrality, and a principle of market microstructure invariance to derive scaling laws expressing bid-ask spreads, transaction costs functions, bet sizes, number of bets, and other financial variables in terms of dollar trading volume and volatility. The scaling laws are tested using data on bid-ask spreads for Russian and U.S. stocks. These scaling laws provide practical metrics for risk managers and traders; scientific benchmarks for evaluating controversial issues related to high frequency trading, market crashes, and liquidity measurement; and guidelines for designing policies in the aftermath of financial crisis.
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November 23, 18:10-19:30
Andrey Lvovich ITKIN ,
The ATM implied skew in the ADO-Heston model
Rough volatility (RV) models increase their popularity since 2007 when it was first shown that for a wide range of assets, historical volatility time-series exhibit a behavior which is much rougher than that of a Brownian motion (BM). One of the important findings of the RV models consists in their ability to reproduce the explosive behavior of the implied at-the-money skew observed empirically when the option maturity goes to zero. On the other hand, the cost one has to pay for getting the advantages of a RV model are technical problems arising due to the non-Markovian nature of the fractional BM.
At the same time, alternative to RV and simpler models have been proposed in the literature, which are Markovian in nature, and, thus, allow solving pricing problems via a well-elaborated approaches, e.g. by solving a PDE. Moreover, recent analysis of market data and numerical experiments show that, even when the instantaneous volatility has diffusive dynamics with the same roughness as the BM, the realized volatility exhibits rough behavior corresponding to a Hurst exponent significantly smaller than 0.5. Also, it is reported that the implied ATM skew does not follow a power law for short maturities and is better captured by simple parametrizations that do not blow up for vanishing maturity.
From the modeling point of view these results mean that, perhaps, market data on realized volatility cannot be used to decide which one - rough or Markovian stochastic volatility model is preferable to replicate the observed market behavior. Therefore, other measures would be useful for this purpose, e.g. the vanilla and forward implied volatilities and skews which could be retrieved from the market data.
In this presentation we discuss the above problems in more detail, and also, following the idea of [P. Carr, A. Itkin, 2019, Risk], describe a new Markovian approximation of the rough Heston model. We show that the behavior of the implied ATM skew in this model is similar to that reported in [M. Amrani, J. Gyon, 2022] with no blow up for vanishing maturity.
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November 30, 18:10-19:30
Evgeny Vladimirovich BURNAEV ,
Doctor of Physical and Mathematical Sciences, Professor, Head of the Center of Applied AI Skoltech, Head of the scientific group, AIRI
Topology strikes back: everything you wanted to know about the shape of your data but were afraid to ask
Real world data has a shape, and a shape "makes a difference." However, standard machine learning methods often do not take into account the shape of the data. In turn, modern methods of topological data analysis just analyze their form as the most important property. The lecture will discuss how topological data analysis works. It will be shown how topological features make it possible to describe the shape of data and significantly increase the efficiency of machine learning models for processing information from seemingly completely different areas - text data and speech data. Based on a new topological measure of similarity, an approach will be described for constructing a low-dimensional description of a data shape that has the property of "disentanglement" - various parameters of this description are automatically responsible for different properties of the data, which makes it possible to increase the interpretability of machine learning models.
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December 07, 18:10-19:30
Viktor ANTIPOV ,
On ruin probabilities with investments in a risky asset
In this paper, we study the asymptotics of the ruin probability in the Cramer — Lundberg model with exponentially distributed payments and capital investment in a risky asset. It is shown how, using the methods of power geometry, one can obtain power asymptotics for solutions of differential equations describing the ruin probability as a function of the initial capital. For the case when the dynamics of an asset is given by a geometric Brownian motion, the corresponding boundary value problems are set and formulas for asymptotic expansions for the ruin probability are obtained. In the case when the parameters of a geometric Brownian motion obey a two-state Markov process, an equation is obtained for the ruin probability asymptotic index.
December 14, 18:10-19:30
Artur SIDORENKO ,
Axiomatic view of the Rogers–Veraart and Suzuki–Elsinger models of systemic risk
An interbank network model with cross-holdings and default costs is studied. Following the approach of Eisenberg and Noe, we define the model using a few natural financial rules and derive a finite family of fixed point problems. These fixed-point problems are parameterized by Boolean cube vectors, which can be interpreted as the propensity of banks to fictitious bankruptcy. The proposed model combines the main properties of the Rogers–Veraart, Suzuki–Elsinger, and Ararat–Meimandzhanov models. Methods are proposed for calculating the maximum and minimum clearing pairs using mixed-integer linear programming and the Gaussian algorithm for eliminating variables.
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You can watch the meetings that took place earlier in the playlist of the Foundation's channel.