Vienna Seminar in Mathematical Finance and Probability

Dieses Seminar wird in kooperation von folgenden Forschungsbereichten / Institutionen organisiert:

Vorträge werden über die FAM-news mailing list, öffnet eine externe URL in einem neuen Fenster angekündigt.

Zukünftige Vorträge

Etwa einmal monatlich an Donnerstags, 15:30 - 18:30 Uhr CEST, in Anwesenheit wenn möglich (ansonsten Online).

2025-03-27

Natalie Packham, öffnet eine externe URL in einem neuen Fenster (Berlin School of Economics and Law, DE)

2025-04-03

Mogens Steffensen, öffnet eine externe URL in einem neuen Fenster (University of Copenhagen, DK)

 

Vergangene Vorträge / Summer Term 2024

2024-08-19
TU Wien, Wiedner Hauptstraße 8, 1040 Wien, "Freihaus" building, green section, 6th floor, seminar room DA green 06A, öffnet eine externe URL in einem neuen Fenster

10:15

Benedict Bauer, öffnet eine externe URL in einem neuen Fenster (University of Vienna)
Martingale Bridges with prescribed domain
Abstract: In discrete time financial markets, a sufficient condition for the absence of arbitrage is the existence of a martingale pricing measure that satisfies market imposed constraints. From a model-free perspective, this leads to investigating the existence of martingale bridges with prescribed domains. However, conventional convex ordering requirements on marginal distributions are insufficient to guarantee their existence. To address this, we reformulate Strassen’s theorem, moving away from the convex envelope approach to one that aligns with the geometry of the prescribed domain. This new formulation gives rise to duality results applicable to robust utility maximization with fixed marginal constraints.
This is joint work with Christa Cuchiero.

11:00

Peter Friz, öffnet eine externe URL in einem neuen Fenster (TU and WIAS Berlin)
On signature moments and cumulants in semimartingale models
Abstract: The concept of signatures and expected signatures is vital in data science, especially for sequential data analysis. The signature transform, a Cartan type development, translates paths into high-dimensional feature vectors. Under natural conditions, the expectation of the signature, a.k.a. signature moments, determines the law of the signature. We are interested in computing expected signatures in a general semimartingale setting. A log-transform leads us to signature cumulants, non-commutative generalizations of classical cumulants. Recursive expressions are given that can be seen as generalizations of recent results by Lacoin–Rhodes–Vargas (PTRF 2023) and F-Gatheral (AOP 2022), motivated by problems in statistical physics and quantitative finance, respectively.
This talk is based on joint work with P. Hager and N. Tapia.

2024-06-27
TU Wien, Wiedner Hauptstraße 8, 1040 Wien, "Freihaus" building, yellow section, 7th floor, seminar room DB gelb 07, öffnet eine externe URL in einem neuen Fenster

16:30

Pavel Shevchenko, öffnet eine externe URL in einem neuen Fenster (Macquarie Business School)
Solving stochastic dynamic integrated climate-economy models
Abstract: The classical dynamic integrated climate-economy (DICE) model has become the iconic typical reference point for the joint modelling of economic and climate systems, where all six model state variables (including carbon concentration, temperature, and economic capital) evolve over time deterministically and are affected by two controls (carbon emission mitigation rate and consumption). We consider the DICE model with stochastic shocks in various parts of the model and solve it under several scenarios as an optimal stochastic control problem.

2024-05-23
TU Wien, Wiedner Hauptstraße 8, 1040 Wien, "Freihaus" building, yellow section, 7th floor, seminar room DB gelb 07, öffnet eine externe URL in einem neuen Fenster

16:00

Martin Friesen, öffnet eine externe URL in einem neuen Fenster (Dublin City University)
Affine Volterra processes: From stochastic stability to statistical inference
Abstract: Recent empirical studies of intraday stock market data suggest that the volatility, seen as a stochastic process, exhibits sample paths of very low regularity, which are not adequately captured by existing Markovian models, such as the Heston model. Additionally, classical affine processes fail to capture the observed term structure of at-the-money volatility skew. Both drawbacks can be addressed by rough analogues of stochastic volatility models described in terms of affine Volterra processes. While the newly emerged rough volatility models have proven themselves to fit the empirical data remarkably, their mathematical properties have not been thoroughly investigated. The absence of the Markov property combined with the fact that these processes are not semimartingales constitute the main obstacles that need to be addressed. In the first part of this presentation, we address the mean-reversion property for continuous affine Volterra processes. Based on a generalized affine transformation formula for finite-dimensional distributions, we prove the existence and uniqueness of stationary processes, characterize their dependence on the initial condition, and subsequently prove the law of large numbers. Afterward, we discuss recent progress on the regularity of the distributions up to the boundary. Based on the ergodicity combined with the regularity of the law, in the last part of this talk we propose a flexible method for the maximum-likelihood estimation of the drift parameters..
This presentation is based on joint works with M. Ben Alaya, L.A. Bianchi, S. Bonaccorsi, P. Jin and J. Kremer.

2024-03-07
University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Wien, SR3, 1st floor

16:45

 

 

Johannes Wiesel, öffnet eine externe URL in einem neuen Fenster (Carnegie Mellon University)
Empirical martingale projections via the adapted Wasserstein distance
Abstract: Given a collection of multidimensional pairs {(Xi,Yi):1≤i≤n}, we study the problem of projecting the associated suitably smoothed empirical measure onto the space of martingale couplings (i.e. distributions satisfying \E[Y|X]=X) using the adapted Wasserstein distance. We call the resulting distance the smoothed empirical martingale projection distance (SE-MPD), for which we obtain an explicit characterization. We also show that the space of martingale couplings remains invariant under the smoothing operation. We study the asymptotic limit of the SE-MPD, which converges at a parametric rate as the sample size increases if the pairs are either i.i.d. or satisfy appropriate mixing assumptions. Additional finite-sample results are also investigated. Using these results, we introduce a novel consistent martingale coupling hypothesis test, which we apply to test the existence of arbitrage opportunities in recently introduced neural network-based generative models for asset pricing calibration.
This talk is based on joint work with Jose Blanchet, Erica Zhang and Zhenyuan Zhang.