Laboratory Seminars

The second part of the talk examines explicit inventory risk management in multi-level market making based on Imitative Market Making. Instead of a fixed penalty for an open position, a constraint is imposed on the expected exposure of the open position, and its enforcement is ensured through Lagrangian primal-dual optimization, cost critics, and calibration of risk estimation. A methodology is presented for comparing Risk-Budgeted IMM with a fixed-penalty approach in terms of the accuracy of achieving a specified risk level and the robustness of results on historical BTC, ETH, and BNB data.

The report considers the training of multi-level market-making strategies with an explicit constraint on the expected exposure on the open position. An extension of the Imitative Market Making approach with risk budgeting is presented, as well as a methodology for its comparison with fixed penalties in terms of risk manageability, economic efficiency, and robustness of results on historical BTC, ETH, and BNB data.

Stochastic optimal control deals with problems in which one is required to intervene in a stochastic system in order to optimize a certain performance criterion. Such problems arise in a wide variety of applied domains, including engineering, economics and finance, computer science, and others. The talk will provide an overview of the core ideas and methods of the theory of stochastic optimal control. We will discuss both classical analytical techniques for solving such problems and contemporary approaches based on deep learning.

The presentation considers a new approach — the AI-GARCH-M model — for modelling the risk premium, building on the direction of GARCH modelling and the ideas of the seminal works [Engle, 1982; Bollerslev, 1986]. The proposed approach allows not only modelling an asymmetric risk premium (as implemented, for example, in [Trifonov, Potanin, 2024]), but also accounts for the impact of extremely high volatility on returns (empirical evidence in favour of such a phenomenon is noted, for instance, in [Black, 1976]). The study carries out numerical verification of some statistical properties of the obtained estimates, as well as a comparison of the proposed approach with existing ones. Special attention is paid to the procedure for estimating the extreme threshold when modelling extremely high volatility (in particular, using methods of extreme value theory).

The talk is devoted to the problem of long-term forecasting of event sequences (e.g., user purchases, transactions, or actions on online platforms). In the standard formulation, a model typically predicts only the next step, but in the long-term forecasting problem, it is required to reconstruct an entire future horizon of events along with their times and types. The work investigates a hybrid approach that combines diffusion modeling of the future fragment and DeTPP — a method that matches predicted events with real ones without rigidly aligning their order. The main goal is to understand when such a combination is truly helpful, which architectural solutions make the model more stable, and which lead to a conflict between the components.

The talk will examine the application of Kolmogorov–Arnold networks (KAN) to derivative pricing, based on two works by Laub. First, splines, function approximations, and the Kolmogorov–Arnold representation will be discussed, followed by an exploration of KAN as neural networks with trainable univariate functions instead of fixed activation functions. In the final part, we will introduce KAFIN, a financially informed KAN model for option pricing, and compare KAN-based approaches with alternative neural network models for function approximation tasks and Black–Scholes pricing.

The study examines the impact of high-frequency trading (HFT) on order flow toxicity and adverse selection risk in the Russian stock market using data from Moscow Exchange. The key metric employed is VPIN, which measures the probability of informed trading through the imbalance of buy and sell orders within volume buckets. Based on regression analysis, the speaker shows that aggressive HFT strategies associated with массов cancellations of orders and rapid reactions increase order flow toxicity, while market-making activity helps reduce it. Less liquid medium-cap stocks were found to be the most sensitive to these effects. In conclusion, the study proposes further development through agent-based modeling of the limit order book (LOB), including simulations with HFT agents to assess the impact of market changes and regulatory measures.

Financial markets are often subject to various forms of manipulation, including pump-and-dump schemes which lead to significant price volatility and financial losses for investors. Previous studies on cryptocurrency markets have used machine learning methods for the early detection of manipulation targets. However, these methods had serious limitations due to imbalances in historical data. To address these issues we propose a new framework for detecting manipulation targets, incorporating two-stage data normalization, algorithm-specific optimization, and novel microstructural features. The present ralk will explore several gradient boosting-based approaches, including hyperparameter optimization accounting for class imbalance and ranking algorithms. The results of the proposed algorithms outperform existing methods, achieving a top-1 accuracy of 22.4% and a top-10 accuracy of 56.9% on a test set with severe class imbalance (the class imbalance ratio is approximately 290).
 

Fractional Brownian motion (fBm) introduced by A.N. Kolmogorov in 1940, is currently one of the key models in the analysis of data with dependence on the past (including the effect of "long memory" or "strong aftereffect"). However, the analytical study of this process is significantly complicated by the fact that fBm is neither a Markov process nor a semimartingale (therefore, classic stochastic methods cannot be applied directly). This report demonstrated approaches that still allow to apply elements of Markov and martingale theories in some form to study the properties of fractional Brownian motion.

The talk was devoted to the theory of optimal stopping — a part of of probability theory that studies problems of choosing the best time to make a decision. The formulations of optimal stopping problems and the main methods for solving them were covered, as well provided examples of applications in mathematical finance. Modern numerical approaches were also discussed including methods based on machine learning.

The seminar examined the application of machine learning methods to predicting asset returns in the cryptocurrency market. Special attention is paid to how the quality of forecasts changes with an increase in the prediction horizon, as well as inter-exchange effects. It was shown that the Binance USDM futures market plays a key role in price formation, and other exchanges mainly reflect the dynamics of Binance with a time lag. Based on these observations, approaches to building features and models for predicting returns were discussed.

The seminar reviewed a comparative study of order flow toxicity on two structurally different platforms: the Binance cryptocurrency exchange and the MOEX regulated stock exchange. High-frequency data was used, and classical toxicity metrics and their first differences were analysed to identify dynamic asymmetries. The prediction of price slippage relative to VWAP using the XGBoost machine learning model was discussed as a proxy indicator of toxicity.

The seminar examined the dynamics of the toxic flow of applications in financial markets and the role of high-frequency trading (HFT) in the formation of adverse selection. Special attention is paid to how fast automated strategies affect the ratio of informed and uninformed market participants, as well as the stability of intraday liquidity.

This project seminar is devoted to the study of methods for personalisation of diffusion models with a limited number of images. The problem of retraining for particular details is considered and the approach of temporary redistribution of diffusion steps—time-step reweighting—is presented. The method uses an uneven distribution of timesteps, focusing on the areas with the most informative features, and adjusts the training weights to maintain unbiasedness. This principle makes it possible to enhance the assimilation of the key characteristics of an object and increase the stability of personalisation without changing the architecture of the model or increasing computational costs.

The seminar examined how multi-agent systems are used to study complex processes in economics and finance. It was shown why historical data alone is not enough to test many hypotheses, and how agent-based simulators can reproduce market dynamics and a system's response to external influences.

The key elements of such models are analysed in detail—the concepts of agent, shock, and the limitations that arise during their construction. Special emphasis is placed on examples of practical application: modelling various behavioural strategies in trading systems, research on automated market makers (AMM), and alternative market mechanisms. The role of liquidity pools and their difference from traditional order book systems is considered separately.

The project seminar is devoted to an in-depth analysis of modern methods of managing neural network generative models. We have reviewed key precision control mechanisms such as IP Adapter, LoRA, and ControlNet, which allow for customisation of the content, style, and pose of the generated image. Special attention is paid to the transition from static images to video through the Animate Anyone and UniAnimate architectures. Computational optimisation methods that are critical for practical application are also touched upon. All this is considered in the context of the applied task of virtualising clothing fitting in e-commerce, where accuracy and realism are key factors.

During the seminar, methods for evaluating hallucinations in the generation of diffusion models were considered. The main focus was on the deterministic method, the essence of which is the mapping of images into a one–dimensional space and clustering in the plane of Complexity-Entropy characteristics for the time series obtained from the images, which makes it possible to assess the degree of confidence in the belonging of the generation to the class of hallucinations.

The study, which was reviewed during the project seminar, analyses bifurcation points in financial models with coloured noise, as well as examines market dynamics involving traders using various strategies. The main focus is on the Vasicek stochastic model, which numerically studies the effect of coloured noise on change-points using machine learning (LSTM) methods. In parallel, a simulation of a single-security market is being considered, where traders adapt their strategies depending on market conditions.

The research results combine the theoretical analysis of stochastic systems with practical modelling of market dynamics, which can be useful for developing sustainable trading algorithms and risk management.

Using an agent-based simulation model, we study how the choice of a liquidity strategy depends on the learning algorithm used by traders. In previous studies on this topic, for dealer-type markets, the result was obtained on the irrelevance of the algorithm used. We find the only non-cooperative Nash equilibrium in our model and show that for two of the three algorithms tested, traders converge to significantly underestimate the liquidity provided compared to the non-cooperative equilibrium strategy.

Fictitious trading (wash trading) remains a serious problem on decentralised exchanges, especially in highly speculative segments such as memecoins, where artificial trading activity distorts liquidity and pricing indicators. Unlike traditional financial markets and centralised exchanges with limit orders, automated market makers (AMM) are based on special mechanisms that require specialised methods for detecting manipulation.

This study suggests a comprehensive approach to detecting fictitious trading on Uniswap v2 using graph analysis, which allows for the adaptation of existing detection methods to the AMM environment. We have collected a unique dataset with historical memecoin trading market data and developed several methods to identify fictitious trades: (1) a heuristic method based on approaches from traditional finance, and (2) two graph methods that model trader interaction in the form of directed graphs to identify fictitious trading cycles. Key graph features such as transaction cycling and address clustering are used to improve detection accuracy.

Evaluation of the proposed methods shows that graph approaches are superior to classical techniques in detecting fictitious trading on AMM exchanges. Our analysis allows us to quantify the volume of fictitious trading in pools and demonstrate its impact on liquidity and price formation. This research contributes to the development of on-chain financial manipulation analytics by offering a scalable, data-driven methodology adapted to manipulation in the AMM environment. The results of the work are valuable for regulators, developers, and users of decentralised exchanges.

The workshop examined white, red, and green noise in financial time series and their impact on the detection of transition points. Stochastic models, including the Ornstein–Uhlenbeck process, and numerical analysis methods such as the Krylov–Bogolyubov averaging were also discussed. Special attention was paid to green noise and its role in irreversible transitions between system states.

In addition, we reviewed transition point detection algorithms (PELT) and machine learning (LSTM, CatBoost) for classifying time series states, and emphasised the importance of choosing a noise model to improve the effectiveness of forecasting and risk management.

The article 'Market Efficiency, Informational Asymmetry and Pseudo-Collusion of Adaptively Learning Agents' was presented and discussed at the seminar. Abstract: We examine the dynamics of informational efficiency in a market with asymmetrically informed, boundedly rational traders who adaptively learn optimal strategies using simple multiarmed bandit (MAB) algorithms. The strategies available to the traders have two dimensions: on the one hand, the traders must endogenously choose whether to acquire a costly information signal, on the other, they must determine how aggressively they trade by choosing the share of their wealth to be invested in the risky asset. Our study contributes to two strands of literature: the literature comparing the effects of competitive and strategic behaviour on asset price efficiency under costly information as well as the actively growing literature on algorithmic pseudo-collusion in financial markets. We find that for certain market environments our results contradict the predictions of Kyle [1989] in that a market with strategically acting traders can be more efficient than a purely competitive one. Furthermore, we obtain novel results on the ability of independently learning traders to coordinate on a pseudo-collusive behaviour, leading to non-competitive pricing. Contrary to some recent contributions (see eg [Cartea et al. 2022]), we find that the pseudo-collusive behaviour in our model is robust to a large number of agents, demonstrating that even in the setting of financial markets with a large number of independently learning traders, non-competitive pricing and pseudo-collusive behaviour can frequently arise. 

Financial markets are often subject to various forms of manipulation, including pump-and-dump schemes, which lead to significant price volatility and financial losses for investors. Previous research on cryptocurrency markets has used machine learning methods to identify manipulation targets early. However, these methods had serious limitations due to imbalances in the historical data. To solve these problems, we propose a new framework for detecting manipulation targets, including two-step data normalisation, specific algorithm optimisation, and new microstructured features. The workshop reviewed several approaches based on gradient boosting, including hyperparameter optimisation based on class imbalance and ranking algorithms. The results of the proposed algorithms surpass existing methods, achieving an accuracy of 5% in the top 1 and 45% accuracy in the top 10 in a test sample with a strong class imbalance (class imbalance is approximately 270).

In the classic work, Grossman and Stiglitz [1980]* show that financial asset prices inevitably contain a certain degree of inefficiency at non-zero information costs. However, this result was obtained in the paradigm of rational expectations, which place unrealistic demands on the rationality of agents, and postulates only the impossibility of effective equilibrium, without affecting the dynamics of market efficiency. Simulation multi-agent models with an element of market selection allow us to study the dynamics of market efficiency in conditions when agents are limited rational and adaptive. We model investor behavior using the so-called multi-armed bandit algorithm and discover a U-shaped ratio of market efficiency to information costs.

* Grossman, Sanford J., and Joseph E. Stiglitz. "On the impossibility of informationally efficient markets." The American economic review 70, no. 3 (1980): 393-408.

A research paper was presented at the seminar, the purpose of which was to analyse the break points in stochastic interest rate models under the influence of coloured noise. The effect of coloured noise on the number of breakpoints and their frequency, as well as the possibility of detecting them using a neural network approach, was investigated. The object of the study was the Vasicek stochastic model, which is used to model interest rates. The research methodology included approximation of numerical solutions of the model by the Euler-Maruyama method, calibration of model parameters, as well as adaptation of the integration step. Methods for detecting breakpoints and their application to the generated data were considered separately. As a result of the study, the results of deep learning models for detecting breakpoints in data generated under the influence of noise are presented.