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Глобальный семинар

Серия встреч с ведущими российскими и зарубежными учеными в области финансовой и актуарной математики. 

Участие могут принять все желающие, пройдя предварительную регистрацию.

Руководителем семинара является д.ф.-м.н., профессор, научный директор Фонда Кабанов Юрий Михайлович.

В расписании возможны изменения

Язык: русский/английский
Формат: онлайн


РАСПИСАНИЕ НА ОСЕННИЙ СЕМЕСТР'22

04 октября, 15:00-16:30

 Арнак ДАЛАЛЯН ,
Профессор Департамента статистики ENSAE Paris,  Директор CREST
 
Approximate sampling from smooth and log-concave densities

Sampling from various kinds of distributions is an issue of paramount importance in statistics since it is often the key ingredient for constructing estimators, test procedures or confidence intervals.

In many situations, the exact sampling from a given distribution is impossible or computationally expensive and, therefore, one needs to resort to approximate sampling strategies. Hence, developing theory providing meaningful nonasymptotic guarantees for the approximate sampling procedures is of high importance, especially in the high-dimensional problems.

This talk reviews some recent progress in this direction by considering the problem of sampling from a distribution having a smooth and log-concave density defined on \(\RR^p\), for some integer \(p>0\). We present nonasymptotic bounds for the error of approximating the target distribution by the one obtained by the Langevin Monte Carlo method and its variants. We illustrate the effectiveness of the established guarantees with various experiments.

Underlying our analysis are insights from the theory of continuous-time diffusion processes, which may be of interest beyond the framework of log-concave densities.


08 октября, 15:00-16:30

 Михаил ЖИТЛУХИН ,
к.ф.-м.н., старший научный сотрудник МИАН им. В.А. Стеклова

Growth optimal strategies in a mean-field market

We consider a model of a financial market which consists of a large agent (the market) and a small agent (an individual investor), who invest money in dividend paying stock. Stock prices are determined by the actions of the large agent, and the small agent is a price-taker. The goal of the work is to find a strategy of the large agent which does not allow a small agent to achieve long-term growth of wealth greater than that of the large agent. The motivation for studying this problem arises from the known empirical fact that it is not possible "to beat" the market in the long run. If one assumes that this fact is true, it can be used to describe long-term behavior of the market.


15 октября, 15:00-16:30

 Александр ВЕРЕТЕННИКОВ ,

On SDE with reflection

An introduction to SDEs with reflection along with Ito's formula with local times will be presented in this talk. Weak and strong solutions as well as weak and strong uniqueness problems will be addressed.


22 октября, 15:00-16:30

 Деан ФАНТАЦЦИНИ ,
Доктор экономических наук, профессор кафедры эконометрики и математических методов экономики МШЭ МГУ им. М.В. Ломоносова

Crypto-Coins and Credit Risk: Modelling and Forecasting Their Probability of Death

This paper examined a set of over two thousand crypto-coins observed between 2015 and 2020 to estimate their credit risk by computing their probability of death. We employed different definitions of dead coins, ranging from academic literature to professional practice; alternative forecasting models, ranging from credit scoring models to machine learning and time-series-based models; and different forecasting horizons. We found that the choice of the coin-death definition affected the set of the best forecasting models to compute the probability of death. However, this choice was not critical, and the best models turned out to be the same in most cases. In general, we found that the cauchit and the zero-price-probability (ZPP) based on the random walk or the Markov Switching-GARCH(1,1) were the best models for newly established coins, whereas credit-scoring models and machine-learning methods using lagged trading volumes and online searches were better choices for older coins. These results also held after a set of robustness checks that considered different time samples and the coins’ market capitalization.


29 октября, 15:00-16:30

 Саид ХАМАДЕН ,
Professor, Laboratoire Manceau de Mathématiques (LMM), Le Mans Université 

Mean-field doubly reflected backward SDEs and zero-sum Dynkin games

We study mean-field doubly reflected BSDEs. First, using the fixed-point method, we show existence and uniqueness of the solution when the data which define the BSDE are $p$-integrable with $p=1$ or $p>1$. The two cases are treated separately. Next by penalization we show also the existence of the solution. The two do not cover the same set of assumptions.


12 ноября, 15:00-16:30

 Миклош РАСОНИ ,
Professor, Renyi Institute, Hungarian Academy of Sciences

Strongly risk-averse investors in mean-reverting market


19 ноября, 15:00-16:30

 Михаил Александрович УРУСОВ ,

Reducing Obizhaeva-Wang type trade execution problems to LQ stochastic control problems

We start with a stochastic control problem where the control process is a process of finite variation with jumps and acts as integrator both in the state dynamics and in the target functional. Problems of such type arise in the stream of literature on optimal trade execution pioneered by Obizhaeva and Wang (models with finite resilience). We consider a general framework where the price impact and the resilience are stochastic processes. Both are allowed to have diffusive components. First we continuously extend the problem from processes of finite variation to progressively measurable processes. Then we reduce the extended problem to a linear quadratic (LQ) stochastic control problem. Using the well developed theory on LQ problems we describe the solution to the obtained LQ problem and trace it back up to the solution to the (extended) initial trade execution problem. Finally, we discuss several examples. Among other things the examples show the Obizhaeva-Wang model with random terminal and moving targets, the necessity to extend the initial trade execution problem to a reasonably large class of progressively measurable processes (it is necessary to go beyond semimartingales!) and the effects of diffusive components in the price impact process and/or in the resilience process. This is a joint work with Julia Ackermann and Thomas Kruse.


26 ноября, 15:00-16:30

 Юрий Михайлович КАБАНОВ ,
д.ф.-м.н., профессор, Председатель Совета, Научный директор Фонда,Член Academia Europaea

Теория разорения со случайными процентными ставками

В докладе будут изложены математические аспекты современной теории разорения, в которой предполагается, что резерв страховой компании инвестирован в рисковый актив со случайной процентной ставкой.

В частности, будет изложена редукция задачи о разорении к асимптотике хвоста распределения случайной величины представимого в виде суммы ряда из нарастающих произведений независимых случайных величин. Эта редукция позволяет получить асимптотику вероятности разорения применением теории Кестена-Голди. Основное внимание будет уделено моделям, в которых процентная ставка является случайным процессом, характеристики которого зависят от состояния экономики. В математической терминологии - это модели со скрытыми марковскими процессами, в финансовой - модели со стохастической волатильностью.


3 декабря, 19:00-20:30

 Чагын АРАРАТ ,
Ph.D.; Assistant Professor, Department of Industrial Engineering, Bilkent University

Dynamic mean-variance problem: recovering time-consistency

The dynamic mean-variance problem is a well-studied optimization problem that is known to be time-inconsistent. The main source of time-inconsistency is that the family of conditional variance functionals indexed by time fails to be recursive. We consider the mean-variance problem in a discrete-time setting and study an auxiliary dynamic vector optimization problem whose objective function consists of the conditional mean and conditional second moment. We show that the vector optimization problem satisfies a set-valued dynamic programming principle and is time-consistent in a generalized sense. Moreover, its weighted sum scalarizations are closely related to the mean-variance problem through simple nonlinear transformations. This is at the cost of using stochastic and time-varying weights in the mean-variance problem. We also discuss the relationship between our results and some recent results in the literature that discuss the use of time-varying weights under special dynamics. Finally, in a finite probability space, we propose a computational procedure that relies on convex vector optimization and convex projection problems, and we use this procedure to calculate time-consistent solutions in concrete market models. Joint work with Seyit Emre Düzoylum (UC Santa Barbara).


10 декабря, 15:00-16:30

 Елена Владимировна БОГУСЛАВСКАЯ ,
Brunel University London, Department of Mathematical Sciences; PhD University of Amsterdam

Интегральные преобразования Аппеля и мартингалы: еще один способ построения мартингалов

В этом докладе мы покажем нетрадиционный способ построения мартингала, достигающего определенного граничного условия в заданный момент времени.

Все, что мы должны знать — это кумулянты основного процесса. Этот подход особенно эффективен для полиномиальных функций в граничных условиях.


17 декабря, 15:00-16:30

 Александр Андреевич ЛЫКОВ ,
Научный сотрудник кафедры теории вероятностей МГУ, кандидат физико-математических наук

On market regimes and adaptive portfolio models

In many areas of finance, the problem of heteroscedasticity is raised. Generally financial time series are not homogeneous. Particularly in portfolio management tasks. To construct more realistic and useful models we should consider time dependent or (and) state dependent models for allocation algorithms. In the talk we will discuss one state dependent model for asset allocation which admits a close solution and can be used to test some hypothesis analytically. We will find some unexpected features of that model in realistic settings. Also, we will discuss different approaches to market regime identifications.


Посмотреть состоявшиеся ранее встречи в рамках Глобального семинара можно в плейлисте канала Фонда. 

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