We would like to cordially invite you to two talks in the Vienna Seminar in Mathematical Finance and Probability (jointly organized with TU Wien and University of Vienna), taking place at WU next Thursday:

Claudio Fontana(Department of Mathematics "Tullio Levi-Civita", University of Padova)
Data-driven Heath-Jarrow-Morton models
Thursday, January 23, 2025, 15:30, WU Campus, Building D4, Room D4.0.127

Abstract:
We develop a data-driven version of Heath-Jarrow-Morton models in the context of interest rate modeling. We consider models driven by a linear functional of the yield curve, such as a family of representative forward rates, possibly augmented by a set of economic factors. The volatility is parameterized by a neural network, the parameters of which are learned by calibration to past market yield curves. This results in a data-driven arbitrage-free model for the prediction of yield curves. Our setup allows for the possibility of scheduled jumps, which can arise from monetary policy decisions. We illustrate our deep learning procedure by reconstructing and forecasting the Euro area yield curves. Based on joint work with Christa Cuchiero (University of Vienna) and Alessandro Gnoatto (University of Verona).

Dörte Kreher(Department of Mathematics, Humboldt-Universität zu Berlin)
On the stochastic porous medium equation with sticky reflected behavior
Thursday, January 23, 2025, 16:45, WU Campus, Building D4, Room D4.0.127

Abstract:
In recent years, a variety of SPDE models have been suggested as macroscopic models for limit order books. In such a context, it is desirable that the infinite-dimensional stochastic system, which models the quantity of placed limit orders, remains non-negative. Moreover, if one also wants to include illiquidity effects in the model, the dynamics should be able to spend a positive amount of time at zero. This motivates to look for SPDEs with sticky reflected behavior at zero, in which case the zero level set may have positive Lebesgue measure. In general, the analysis of sticky reflected diffusions is challenging due to the discontinuity of the diffusion coefficient and the sojourn coefficient at the reflection boundary. In this talk, I will show how non-negative martingale solutions of a certain SPDE, the stochastic porous medium equation, with sticky reflected behavior at zero can be constructed. The construction follows by the stochastic Faedo-Galerkin method and employs an Aubin-Lyons type interpolation argument for Sobolev spaces with different space-time regularity to derive the required moment estimates. The talk is based on joint work with B. Hambly and K. Starovoitovs.

For further information and the seminar schedule, please visit:
https://fam.tuwien.ac.at/events/vs-mfp/