# Global Seminar

Anyone can participate by registering in advance.

*The schedule is subject to change.*Language: Russian/English

Format: online

**THE SCHEDULE FOR FALL**

**'22**

**October 4, 3 p.m.- 4:30 p.m. (Moscow time)**

Arnak S. Dalalyan ,

Professor of Statistics at ENSAE Paris, Director of 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.

**October**

**8, 3 p.m.- 4:30 p.m. (Moscow time)**

Mikhail Zhitlukhin ,

Senior Researcher, Steklov Institute of Mathematics (Russian Academy of Sciences)

**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.

**October 15, 3 p.m.- 4:30 p.m. (Moscow time)**

Alexander Veretennikov ,

**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.

**October 22, 3 p.m.- 4:30 p.m. (Moscow time)**

**Dean Fantazzini ,**

**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.

**October 29, 3 p.m.- 4:30 p.m. (Moscow time)**

Saïd HAMADENE ,

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.

**November 12, 3 p.m.- 4:30 p.m. (Moscow time)**

**Miklós Rásonyi ,**

Professor, Renyi Institute, Hungarian Academy of Sciences

**Strongly risk-averse investors in mean-reverting market**

**November 19, 3 p.m.- 4:30 p.m. (Moscow time)**

**Mikhail URUSOV ,**

**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.

**November 26, 3 p.m.- 4:30 p.m. (Moscow time)**

Yuri KABANOV ,

Chairman of the Board, Scientific Director of the Foundation, Dr. Sci. in Phys. and Maths, Professor, Member of Academia Europaea

**Ruin theory with random interest rates**

The lecture will outline the mathematical aspects of the modern ruin, which assumes that the insurance company invests its reserve in a risky asset paying a random interest rate.

In particular, we will present a reduction of the ruin problem to the study of asymptotical behavior of the tail of distribution of the sum of series of increasing products of independent random variables. This reduction makes it possible to obtain the asymptoticsof the ruin probability using the Kesten-Goldie theory. The main attention will be paid to models in which the interest rate is a random process, the characteristics of which depend on the state of the economy. In mathematical terminology, they are called hidden Markov models; in financial terminology, they are referred to as models with stochastic volatility. We concentrate our efforts on understanding "technical" issues of various approaches

**December 3, 7 p.m.- 8:30 p.m. (Moscow time)**

Çağın ARARAT ,

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).

**December 10,**

**3 p.m.- 4:30 p.m. (Moscow time)**

Elena BOGUSLAVSKAYA ,

Brunel University London, Department of Mathematical Sciences; PhD University of Amsterdam

**Appell integral transforms and martingales: yet another way to construct martingales.**

In this talk we show an unconventional way to construct a martingale reaching a particular boundary condition at a particular time.

All we should know is the cumulants of the underlying process. This approach is especially effective with polynomial functions in boundary conditions.

**December 17, 3 p.m.- 4:30 p.m. (Moscow time)**

Alexander LYKOV ,

**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.

*Global Seminar*

*meetings*in the Foundation's channel playlist.