Josef Teichmann

Professor in the Department of Mathematics at ETH Zurich.

Title: The geometry of blurring – diffusion models under geometric constraints 

Abstract: We analyze generative technologies like diffusion models under global geometric constraints on the generated samples.

Ostap Okhrin

Professor, Vice Dean of the “Friedrich List” Faculty of Transport and Traffic Sciences, TUD Dresden University of Technology, Germany

Title:
Learning Low-Frequency Risk Functionals from High-Frequency Financial Data: From Heston Volatility to Skewness and Quantiles

Co-Authors: Haozhe Jiang (TUD) and Michael Rockinger (Uni Lausanne)

Abstract: High-frequency financial data contain rich information about the latent dynamics of returns, volatility, and tail risk. However, classical estimators of low-frequency risk characteristics often rely on nonlinear plug-in ratios, long historical panels, or stationarity assumptions that are difficult to justify in practice. In this talk, I discuss a simulation-based framework for estimating low-frequency distributional functionals from high-frequency observations.

The starting point is the Heston stochastic volatility model, where high-frequency data can be used to estimate spot volatility and the parameters of the latent variance process. This setting highlights both the potential and the difficulty of high-frequency inference, in particular under realistic parameter configurations in which the Feller condition may be violated. Building on these insights, we propose a High Frequency Network, a convolutional neural network architecture that maps intraday returns and their powers directly to monthly realized skewness. Instead of estimating separate moment components and forming unstable ratios, the network learns the low-frequency functional itself from simulated stochastic-volatility paths. Monte Carlo experiments show that this approach reduces finite-sample bias and remains robust under model misspecification, including jump-diffusion dynamics.

Finally, I outline ongoing work extending the same idea to the estimation of low-frequency quantiles. The broader aim is to combine stochastic-process models, high-frequency data, and machine-learning architectures to obtain stable estimators of distributional risk measures relevant for financial econometrics and risk management.

Anton Yurchenko-Tytarenko

Senior Market Analyst Statkraft Energi AS, Norway 

Title: Least squares Monte Carlo for pricing, hedging, and calibration in stochastic market models

Abstract: Modern financial markets exhibit complex phenomena that simple models cannot capture. Replicating these features requires sophisticated stochastic frameworks: rough volatility models, for instance, are widely used to reproduce the implied volatility smiles and skews observed in real markets. 

However, increased realism comes at a price. Complex models, even when they admit simulation via Euler-type discretization schemes, typically lack closed-form expressions for option prices or hedging quantities. This gap creates significant practical challenges. Without analytic pricing formulas, calibrating model parameters to observed option price curves becomes a difficult task. At the same time, classical Monte Carlo methods, while flexible, are computationally too slow for real-time applications such as dynamically updating a hedging portfolio during trading.

In this talk, we discuss the Least Squares Monte Carlo (LSMC) method as a flexible and efficient framework to address these challenges. The approach proceeds in two stages: one first simulates a large ensemble of model trajectories across a range of model parameters, and then applies machine learning techniques to learn how the quantity of interest depends on those parameters. The resulting surrogate is fast to evaluate and well-suited for tasks such as real-time model calibration against market data.

Alexander Kukush

Doctor of science, Professor, Leading researcher at Institute of Mathematics NAS of Ukraine

Title: Nominal-gain tontine fund with a heterogeneous cohort

Abstract: We investigate tontine funds with a heterogeneous cohort of participants. At time 0, each participant makes an initial investment 𝜋_𝑖 in the fund. At time 1, each surviving participant receives a part of the fund, proportional to the number of tontine shares (or protection units) 𝑓_𝑖 appointed to him at time 0. The tontine fund is self-financing in the sense that the total input in the fund (i.e., the total amount of initial investments) equals the total output from the fund (i.e., the total payments, also called compensations, to the survivor). Two versions of the tontine fund are considered: the case with an active administrator and the case with a passive one.

It is shown that under mild conditions the following results hold:
(a) Given the tontine shares 𝑓_𝑖 and given total amount of initial investments, there exists a unique actuarially fair tontine fund, i.e., a fund where the initial investment 𝜋_𝑖 of each participant 𝑖 is equal to his expected compensation.
(b) Given the initial investments 𝜋_𝑖 , there exists a unique choice of tontine shares 𝑓_𝑖 (up to a constant proportion factor) so that the tontine fund is actuarially fair.

The tontine fund considered so far is a so-called ‘nominal payoff’ tontine fund. We also consider ‘nominal gain’ tontine funds where the initial investments are used to pay every survivor his initial investment 𝜋_𝑖 back and where the investments of the deceased participants are proportionally distributed among alive participants, according to the tontine shares 𝑓_𝑖 appointed at time 0. Similar results as for nominal payoff tontine funds are presented for this class of for nominal gain tontine funds.

Further, we show that given the total amount that each participant spends to pay an initial investment in a tontine fund and a premium to buy insurance, combining a tontine fund with a standard insurance contract, one can achieve a less risky compensation (i.e., tontine compensation and insurance payment) compared with a ‘pure’ insurance case. Here, the riskiness of random losses is compared using the convex ordering.

Finally, we study tontine funds when the number of participants grows. This allows evaluation of the limiting compensations and investigation of the asymptotic actuarial fairness of tontine funds. A particular case of a tontine fund composed of several homogeneous tontine funds is studied in detail.

The results are co-authored with Prof. Dr. Jan Dhaene, K.U.Leuven, Belgium.