'Where Accurate Prediction of the Outcome Is Impossible, Stochastic Methods Come into Play'

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The Laboratory of Stochastic Analysis and its Applications at HSE University studies systems and events in which randomness plays a central role. The goal is to predict various phenomena and how they evolve over time. The HSE News Service interviewed the laboratory's head Vladimir Panov and its academic supervisor Valentin Konakov.

— When was the laboratory established?

Vladimir Panov

Vladimir Panov: It was founded in 2014 after winning a competition to establish international laboratories. The laboratory grew out of Prof. Valentin Konakov’s long-standing collaboration with several prominent international scientists.

We then invited Enno Mammen (Germany), Alexander Veretennikov (UK), Stéphane Menozzi (France), and Denis Belomestny (Germany) to join us. Later, many other international researchers became involved in our projects. For ten years, our academic supervisor was Stanislav Molchanov, Professor at the University of North Carolina at Charlotte, USA.

Prof. Konakov led the laboratory until 2025. At the end of that year, he was appointed academic supervisor of the laboratory, handing over the role of laboratory head to me.

— What are the laboratory's main areas of focus?

Vladimir Panov: I would highlight four main areas. The first is modelling jump-type processes (Lévy processes), with applications to financial time series. The second focuses on stochastic differential equations, in particular McKean–Vlasov equations, the approximation of their solutions, and the use of the parametrix method. The third area covers problems in financial and actuarial mathematics. And finally, mean-field game theory. Overall, we work across a range of areas aligned with international research in stochastics. A good sense of current trends in the field can be gained from the section titles at major international conferences.

Valentin Konakov

Valentin Konakov: Another area our colleagues at the laboratory are working on involves quantum equations and fractional stochastic analysis. We focus on topics within stochastics that are of particular interest to the international research community, and these areas indeed attract considerable attention.

— How would you explain stochastic analysis and its basic principles to a layperson with a limited mathematical background?

Vladimir Panov: The term 'stochastics' comes from the Greek word stochazomai, meaning 'guess' or 'assume.' Broadly speaking, anything related to probabilistic analysis can be described as stochastic. Its problems arise whenever we cannot study an object or process using deterministic functions, as we are accustomed to from school mathematics.

Valentin Konakov: In many mathematical problems, as well as in physical, biological, and financial models, the behaviour of a system is often determined by a vast number of random events that cannot be calculated with precision. For example, a particle (such as a bacterium) placed in an apparently still liquid begins to move because it is constantly being pushed from different directions by the surrounding molecules.

The effect of each individual push cannot be measured due to the enormous number of simultaneous interactions, but mathematical and physical methods allow us to account for their combined effect and describe the particle’s motion, which is random but has well-defined statistical properties

Vladimir Panov: Let’s take a simple example. Suppose you have become wealthy and decide to buy a pond, whose value depends directly on the number of fish it contains. To estimate the fish population, you would need to catch them all, but for obvious reasons this is impossible. Instead, you decide to catch some of the fish, tag them, and release them back into the pond. The tagged fish mix with the rest, and you then collect another sample and calculate the proportion of tagged fish. By repeating this experiment several times, you obtain a sample from a hypergeometric distribution. Using methods of mathematical statistics, the total number of fish in the pond can then be estimated from this sample.

Where accurate prediction of the outcome is impossible, stochastic methods come into play. Even when we toss a coin, its motion is not truly random. Everything is governed by the laws of physics: the coin moves under the influence of gravity and the force imparted by the throw. However, trying to describe its motion with precision is extremely challenging. Even with the help of a modern computer, it is difficult to construct an equation that captures all aspects of a coin’s rotation. The outcome depends on multiple factors, including the angle of the hand, the height of the toss, and the way the coin is accelerated. In practice, we can only observe whether the coin lands heads or tails.

If we consider problems in medicine or finance, we see that they involve a significant number of stochastic elements

For example, in finance, a share price depends on multiple participants in the stock market, and it is extremely difficult to predict it using a deterministic function. Therefore, we study the outcome of interactions between all market participants—namely, fluctuations in the share price.

— What are the key objectives then?

Vladimir Panov: Analysing the results of experiments, selecting models to capture their essential features, and drawing meaningful conclusions that can be expressed in terms understandable to economists and specialists in other fields. Sometimes we cannot fully explain why a particular phenomenon occurs, but stochastic analysis allows us to predict how it will evolve over time.

For example, we cannot explain why a stock price is what it is at a given moment, but we can predict that it will fluctuate within a certain range.

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Valentin Konakov: The goal is to predict various phenomena and how they are likely to evolve. Modern reality is the outcome of complex processes that we can observe and attempt to forecast.

— Is your activity mainly focused on applied or basic research? Is it challenging to maintain a balance between the two?

Valentin Konakov: It is primarily focused on basic research. Maintaining a balance is challenging, but circumstances encourage it, and we are now making significant efforts to advance applied research as well.

Vladimir Panov: In many ways, the initiative comes from students who want to see the results of their research as quickly as possible. However, one should not focus exclusively on solving practical problems. Otherwise, there is a risk of reducing all research to mere application of AI methods.

It is important to give students the opportunity to prove themselves. While working on applied projects, they often become interested in deeper research and more fundamental problems.

— Outside of fundamental mathematics, what other areas can apply the principles of analysis and modelling that you study?

Vladimir Panov:

We are currently working on a project in which we apply methods based on jump-type processes to model and forecast inflation and to analyse the value of cryptocurrencies

We also work closely with a team of oncologists at leading cancer clinics. They use methods of stochastic analysis to study factors that contribute to reducing the risk of recurrence after successful cancer treatment. There are other promising areas for research in this field as well. These include, for example, selecting the most appropriate hormone therapy to help women conceive and give birth after overcoming cancer.

Valentin Konakov: Our colleague Vasili Kolokoltsov has obtained notable results in developing models of inspection and corruption in the context of environmental protection (for example, illegal logging). He has derived a new mathematical result we can refer to as the quadratic penalty principle, which shows that corruption can be effectively deterred by introducing fines that increase quadratically with the amount of illegally obtained income.

We are also applying for a grant jointly with the Beijing Institute of Technology to collaborate with our Chinese colleagues on fractional analysis studies.

— Could you explain what this is?

Vladimir Panov: Classical mathematical analysis is based on the properties of functions and the theory of integration. When we extend similar frameworks to random processes and functions, new mathematical objects emerge, and fractional analysis becomes necessary to study them. This approach significantly broadens the mathematical toolkit compared to traditional methods.

— Which of your colleagues' achievements are you proud of?

Vladimir Panov: Over the past 12 years, our laboratory has established itself as a leading centre among Russian laboratories and academic departments working in stochastics.

We have assembled a strong team, including seven Doctors of Sciences and four researchers with PhD degrees

Valentin Konakov: We work on modern, cutting-edge research topics, and new colleagues continue to join our team. For example, Cédric Bernardin, a professor at the HSE Faculty of Mathematics, has been working at our laboratory since March 2026. Before moving to Russia, he was a professor at Université Côte d’Azur in Nice and a researcher at the National Centre for Scientific Research (CNRS) at École Normale Supérieure de Lyon.

— What has changed in the work of the laboratory in recent years? What new areas of research and academic cooperation have taken priority?

Vladimir Panov: Since January of this year, we have established applied research groups: two in finance and one in medicine. This is a long-term project that involves many of our research assistants, students from the Faculty of Economics.

— How do you approach maintaining and advancing international research cooperation?

Vladimir Panov: The focus of international cooperation has, of course, shifted towards the East, and we have been developing collaborations with China and several other countries. Recently, a Russian–Chinese symposium on probability theory was held, in which I took part together with Jean-François Médi Jabir and a number of our early-career researchers.

Valentin Konakov: We continue to organise international conferences at a very high level. The most recent conference was held from April 20 to 24 and was attended by researchers from eight countries. We also aim to participate in international conferences hosted by research centres abroad.

— How do you feel about the use of artificial intelligence?

Vladimir Panov: I once participated in a project testing one of the popular neural networks. I was responsible for a set of problems in probability theory and mathematical statistics. The proportion of tasks that the neural network solved correctly and for which it could justify its reasoning without major errors was relatively small—about 14%. This suggests that the capabilities of AI are still limited. However, it can be useful for routine tasks, such as searching for articles on a given topic. It is important that AI is applied by a skilled user.

Valentin Konakov: Often, AI-generated responses turn out to be incorrect, so it is essential to verify the information it provides.

— Which departments and research centres at HSE University do you interact with?

Valentin Konakov: We work most closely with the Faculty of Mathematics. For many years, we have been running a joint seminar with its professors. I help them identify interesting speakers and invite international colleagues from leading research centres.

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— How are the results of your work applied in the educational process?

Vladimir Panov: Researchers who dedicate themselves to science have a deep understanding of their field and are able to explain it clearly using insightful examples. This depth of understanding is extremely important. It is valuable that students learn from scientists who have studied their discipline in depth.

We have always actively collaborated with the Faculty of Economic Sciences, and a year ago we became part of it as a subdivision. Our staff members teach 12 courses at the faculty.

Under our auspices, the Master’s Programme 'Stochastic Modelling in Economics and Finance' was launched and has been attracting strong interest from applicants for more than 10 years

This confirms that the laboratory’s potential is actively integrated into the educational process.

In turn, the faculty provides financial support for our seminars and summer schools. In addition, two of our research assistants won a grant competition for students, including doctoral students, of the Faculty of Economic Sciences.

— How much in demand are early-career specialists in your field?

Valentin Konakov: There is strong demand in the labour market for specialists in stochastics. This creates certain challenges for us, as we train highly qualified professionals who, after defending their dissertations, often go on to work in banks, insurance companies, and other financial institutions. However, students who wish to pursue science continue to join us, and we hope to further nurture their interest in an academic career.