-2025.05.27.: Sztochasztikus modellezés workshop: május 27-én kedden 16 órakor a 3.218-ban vagy online (a link a program végén található).
Program:
16:00-16:30 Rásonyi Miklós: Convergence of smooth random variables
We establish relationships between rates of weak convergence (as measured by various metrics such as the Wasserstein metric) and rates in a stronger sense, in (weighted) total variation distance.
Using tools from Fourier analysis, we show that, for sufficiently smooth random variables these rates can be compared. Among several applications we will highlight Malliavin calculus and machine learning, where optimization algorithms can be analysed using our approach.
16:35-17:05 Ivkovic Iván: Navigating Geopolitical Turbulence and Shocks: A Dynamic and Data-Driven Perspective
Geopolitical risk has emerged as a dominant driver of global financial volatility, yet existing indices often fail to fully capture its latent, systemic dimensions across asset classes. We propose a novel multi-layered framework for the aggregation, detection, and forecasting of geopolitical risk based on a dynamic interplay between econometric modeling, stochastic volatility theory, and machine learning. Our first methodological layer employs a policy-oriented country-weighted aggregation of ETF and FX volatilities, anchoring the analysis in macro-financial fundamentals. The second layer introduces a PCA-based latent volatility index, extracted from both raw returns and volatility series, capturing co-movements and systemic stress through leading eigenvalue dynamics. Extending this approach, we develop Dynamic Factor Models with time-varying loadings and regime-switching structures, where the latent factor volatility itself evolves according to stochastic differential equations, enhancing both theoretical robustness and empirical flexibility. To assess risk spillovers, we integrate Diebold-Yilmaz network connectedness metrics, mapping the directional transmission of geopolitical shocks. Finally, we propose scenario generation based on Wasserstein Generative Adversarial Networks (GANs) to forecast tail-risk scenarios under extreme geopolitical conditions. This interdisciplinary framework unifies financial mathematics, machine learning, and systemic risk modeling into a forward-looking platform for real-time geopolitical volatility monitoring and stress testing.
17:10-17:40 Nagy Lóránt-Toffalini Leonardo: Reinforcement learning driven trading in stylized markets
Algorithmic trading is a vibrant research area at the interface of academia and industry. Our recent research focuses at bridging reinforcement learning theory and quantitative finance to explore trading policies in an artificial financial environment where the price of a single risky asset follows fractional Brownian motion, and in which the phenomenon of market friction is incorporated.

Building on results by Guasoni, Nika, and Rásonyi [1] we benchmark artificial trading algorithms which were learned by an agent through reinforcement learning.

The work in progress shows that for a reasonable horizon, and anti-persistent price dynamics, the theoretical rates are achieved by an artificial agent using the Proximal Policy Optimization algorithm within a few million training steps.

[1] Guasoni, Paolo and Nika, Zsolt and Rasonyi, Miklos, Trading Fractional Brownian Motion (November 6, 2018)

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