Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Institut für Mathematik

FS Stochastische Analysis und Stochastik der Finanzmärkte

Bereich für Stochastik


P. BANK, Ch. BAYER, D. BECHERER, P. FRIZ, S. KASSING, U. HORST, D. KREHER

 
Das Seminar findet  an der TU Berlin, Institut für Mathematik, Raum MA 042 (Straße des 17. Juni 136) statt. 
 
Zeit: Donnerstag, 16 Uhr c.t. / 17 Uhr c.t.

       

 

 

 

 

 

 

 

24.04.2025

 

N.N.

 

 

 

15.05.2025

16 Uhr c.t.

 
Paul Eisenberg  (Wirtschaftsuniversität Wien)
Natural finite dimensional HJM models are NON-affine

 

Abstract: A zero coupon bond is a contract where one party offers a fixed payment at a pre-specified time point which is called its maturity. A forward rate curve is a theoretical function that encodes the prices of all possible bonds with varying maturities at one given point of time. There are various models that explain the behaviour of forward rate curves accross time. The most principle model in this direction is the Heath Jarrow Morton (HJM)-model which models the forward rate curve directly. This model is known to be free of arbitrage if and only if the HJM-drift condition holds. We are interested in finite dimensional HJM-models which stay on one fixed given finite dimensional manifold, roughly spoken this means that the model stays within a fixed finitely parametrised family of curves. It is well known, that a curve valued process can only stay on a prescribed manifold if the Stratonovich drift is tangential to the manifold at all time, or more simply, if we can instead find a
parameter process which selects the curve seen at a given time. From a statistical point of view it would be desirable to leave the diffusion coefficient of the parameter process open for estimation, or in the language of manifolds that means that any tangential diffusion coefficient should be left open as possible. In this presentation, we find those finite dimensional manifolds where the diffusion coefficient remains fully open for estimation while still allowing for the HJM-drift condition to be met. It turns out that the resulting manifolds are nowhere locally affine. More so, they are nowhere affinely foliated as has been suggested by earlier work (however under different assumptions).

 

  

15.05.2025

17 Uhr c.t.
Thorsten Schmidt  (Universtät Freiburg) 
Insurance-finance markets

 

Abstract: Pension products and long-term insurance policies play a crucial role in our societies. This talk explores approaches for their cost-effective production through investments in financial markets. The key tool here is to link financial and insurance strategies to an appropriate fundamental theorem. To address the risks and uncertainties inherent in such investments, we draw on methods from financial mathematics and the framework of Knightian uncertainty. We will discuss recent developments in this field, highlighting their implications for the sustainable and resilient structuring of pension and insurance products.

 
 

 

22.05.2025

16 Uhr c.t.

 

 

Yang Yang(HU Berlin)

Optimal Control of Infinite-Dimensional Differential Systems with Randomness and Path-Dependence

 

Abstract: This talk is devoted to the stochastic optimal control problem of infinite-dimensional differential systems allowing for both path-dependence and measurable randomness. As opposed to the deterministic path-dependent cases studied by Bayraktar and Keller [J. Funct. Anal. 275 (2018) 2096–2161], the value function turns out to be a random field on the path space and it is characterized by a stochastic path-dependent Hamilton-Jacobi (SPHJ) equation. A notion of viscosity solution is pro- posed and the value function is proved to be the unique viscosity solution to the associated SPHJ equation.

 

 

 

22.05.2025

17 Uhr c.t.

 

 

Johannes Wiesel (Carnegie Mellon University)

Bounding adapted Wasserstein metrics

 

Abstract: The Wasserstein distance Wp is an important instance of an optimal transport cost. Its numerous mathematical properties as well as applications to various fields such as mathematical finance and statistics have been well studied in recent years. The adapted Wasserstein distance AWp extends this theory to laws of discrete time stochastic processes in their natural filtrations, making it particularly well suited for analyzing time-dependent stochastic optimization problems.
While the topological differences between AWp and Wp are well understood, their differences as metrics remain largely unexplored beyond the trivial bound Wp ≲ AWp. This paper closes this gap by providing upper bounds of AWp in terms of Wp through investigation of the smooth adapted Wasserstein distance. Our upper bounds are explicit and are given by a sum of Wp, Eder’s modulus of continuity and a term
characterizing the tail behavior of measures. As a consequence, upper bounds on Wp automatically hold for AWp under mild regularity assumptions on the measures considered. A particular instance of our findings is the inequality AW1 ≤ C√W1 on the set of measures that have Lipschitz kernels. Our work also reveals how smoothing of measures affects the adapted weak topology. In fact, we find that the topology induced by the smooth adapted Wasserstein distance exhibits a non-trivial interpolation property, which we characterize explicitly: it lies in between the adapted weak topology and the weak topology, and the inclusion is governed by the decay of the smoothing parameter.
This talk is based on joint work with Jose Blanchet, Martin Larsson and Jonghwa Park.

 

 

 

05.06.2025

16 Uhr c.t.

 

 
Julian Sester (National University Singapore)     

Distributionally robust Deep Q-Learning and application to portfolio optimization

 

Abstract: 

We propose a novel distributionally robust Q-learning algorithm for the non-tabular case accounting for continuous state spaces where the state transition of the underlying Markov decision process is subject to model uncertainty. The uncertainty is taken into account by considering the worst-case transition from a ball around a reference probability measure. To determine the optimal policy under the worst-case state transition, we solve the associated non-linear Bellman equation by dualising and regularising the Bellman operator with the Sinkhorn distance, which is then parameterized with deep neural networks. This approach allows us to modify the Deep Q-Network algorithm to optimise for the worst case state transition.
We illustrate the tractability and effectiveness of our approach through several applications, including a portfolio optimisation task based on S&P 500 data.
(This is joint work with Chung I Lu and Aijia Zhang)
 
 

 

 

19.06.2025

 

 
Min Dai (The Hong Kong Polytechnic University)
Option Exercise Games and the q Theory of Investment

 

Abstract: 

Firms shall be able to respond to their competitors’ strategies over time. Back and Paulsen (2009) thus advocate using closed-loop equilibria to analyze classic real-option exercise games but point out difficulties in defining closed-loop equilibria and characterizing the solution. We define closed-loop equilibria and derive a continuum of them in closed form. These equilibria feature either linear or nonlinear investment thresholds. In all closed-loop equilibria, firms invest faster than in the open-loop equilibrium of Grenadier (2002). We confirm Back and Paulsen (2009)’s conjecture that their closedloop equilibrium (with a perfectly competitive outcome) is the one with the fastest investment and in all other closed-loop equilibria firms earn strictly positive profits. This work is jointly with Zhaoli Jiang and Neng Wang.

 

 

03.07.2025

16 Uhr c.t.

 
Sören Christensen (Christian-Albrechts-Universität zu Kiel)                   

tba

 

Abstract: 

 

 

 

03.07.2025

 

 
Mathieu Lauriere (NYU Shanghai)

tba

 

17.07.2025

17 Uhr c.t.

 

N.N. 

 

 

 

 

 
 

 

 

 

 

 

 
 

 

 

 

 

 
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Für Rückfragen wenden Sie sich bitte an:

Frau Sabine Bergmann

bergmann@math.hu-berlin.de
Telefon: 2093 45450
Telefax: 2093 45451