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

FS Stochastische Analysis und Stochastik der Finanzmärkte

Bereich für Stochastik


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

 
Das Seminar findet im Sommersemester 2023  an der TU Berlin, Institut für Mathematik, Raum MA 042 - Mathematikgebäude (Straße des 17. Juni 136, 10623 Berlin) statt. 
 
Zeit: Donnerstag, 16 Uhr s.t. / 17 Uhr s.t.

       

 

 

 

 

 

 

 

27.04.2023

 

Christian Kappen & Sebastian Schlenkrich (dfine)

Practical Applications of Machine Learning in Risk and Pricing

        

Abstract: 

Machine Learning (ML) provides techniques for universal function approximation. In this talk, we apply such techniques to the acceleration of complex derivatives pricing, focusing on Value-at-Risk computations for Bermudan interest rate options. We introduce different applicable ML methods, and we present results from our client projects. Moreover, we propose ways to address regulatory requirements via the model lifecycle process. d-fine is a European consulting company with over 1,000 employees. Our projects focus on quantitative issues around data analytics, data science, modelling and the development of sustainable technological solutions

 

11.05.2023

16 Uhr s.t.

 

Denis Belomestny (U Duisburg-Essen)

Reinforcement Learning for Convex MDPs with application to hedging and pricing

 

Abstract: 

Convex MDPs generalize the standard reinforcement learning (RL) problem formulation to a larger framework that includes many supervised and unsupervised RL problems, such as apprenticeship learning, constrained MDPs, and so-called ‘pure exploration’. We consider the reformulation of the convex MDP problem as a min-max game involving policy and cost (negative reward) ‘players’, using duality. Then we study the application of this strategy to pricing and hedging in Pricing/Hedging under optimized
certainty equivalents (OCEs) which is a family of risk measures widely used by practitioners and academics. This class of risk measures includes many important examples, e.g. entropic risk measures and average value at risk.

 

11.05.2023

17 Uhr s.t.

Eyal Neumann (Imperial College London)

Equilibrium in Infinite-Dimensional Stochastic Games with Mean-Field Interaction

                              

Abstract: 

We consider a general class of finite-player stochastic games with mean-field interaction, in which the linear-quadratic objective functional includes linear operators acting on square-integrable controls. We propose a novel approach for deriving explicitly the Nash equilibrium of the game by reducing
the associated first order conditions to a system of stochastic Fredholm equations of the second kind and deriving their closed-form solution. Furthermore, by proving stability results for the system of Fredholm
equations, we derive the convergence of the equilibrium of the N-player game to the corresponding mean-field equilibrium. As a by-product of our results we also derive epsilon-Nash equilibrium for the mean-field game and we show that the conditions for existence of an equilibrium in the mean-field limit are significantly less restrictive than in the finite-player game. Finally we apply our general framework to solve various examples, such as stochastic Volterra linear-quadratic games, models of systemic risk and advertising with delay and optimal liquidation games with transient price impact.
The talk is based on a joint work with Eduardo Abi-Jaber and Moritz Voss.

 

 

25.05.2023

16 Uhr s.t.

Tahir Choulli (U Alberta)

Risk Quantification, Optimal Stopping and Reflected BSDEs for a
Class of Informational Markets

 

Abstract: 

 
We consider the informational model given by the quintuplet (Ω, G, F, τ, P ). Here (Ω, G, P ) is a complete probability space, F is the “public” flow of information, and τ is an arbitrary random time which might not be observable via F. This random time represents default time of a firm in credit risk, or the death time of an insured in life insurance where mortality and/or longevity risks pose serious challenges, or any occurrence time of events that might impact the market somehow. By considering the flow G that incorporates F and makes τ observable when it occurs, we obtain two systems SInit := (Ω, F, P ) and SInf := (Ω, G, P ) called initial system and informational system
respectively, and representing the two groups of agents. In this setting, our main interest lies in quantifying –and possibly classifying– all risks in SInf . More importantly, we want to quantify –and possibly classify– each of the three intuitive classes of risks, namely the risks coming from τ and not
from SInit, the risks from SInit, and the correlation risks resulting from the interplay between SInit and τ . The impact of our answers to this quantification and classification risks seems to be huge as it opened up several directions in the setting of informational markets cited above (i.e. credit risk and life insurance). In this spirit, we can cite the direction of arbitrage theory in these informational frameworks, the optimal portfolio problem in these informational settings, the pricing and/or hedging
problems, ..., etcetera. In this talk, besides the quantification results, I will address a small “portion’ of the two latter problems of pricing and hedging if time permits it. In particular, I will focus on two resulting and intimately related mathematical problems, which are the optimal stopping problem
under stopping with an arbitrary random time and an obtained class of reflected BSDEs. This talk is based on joint works with Safa’ Alsheyab/ Ella Elazkany /Sina Yansori (U of Alberta), and Chaterine Daveloose/Michele Vanmaele (Ghent University).

 

 

08.06.2023

17 Uhr s.t.

 

Paul Hager (HU Berlin)

 

Abstract:

We consider a novel class of portfolio liquidation games with market drop-out ("absorption"). More precisely, we consider mean-field and finite-player liquidation games where a player drops out of the market when her position hits zero. In particular, round trips are not admissible, which can be viewed as a no-statistical arbitrage condition. The equilibrium is seen to be characterized as the unique solution to a higher-order, non-linear integral equation with an endogenous terminal condition. We further show the convergence of the finite player to the mean-field equilibrium. We illustrate the impact of the drop-out constraint on equilibrium trading in several numerical examples. This is a joint work with Guanxing Fu and Ulrich Horst.

 

22.06.2023

 

Mehdi Talbi (ETH Zürich)

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06.07.2023

16 Uhr s.t.

Gudmund Pammer (ETH Zurich))

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06.07.2023

17 Uhr s.t.

Yves Achdou (U Paris-Diderot)

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20.07.2023

16 Uhr s.t.

Annika Kemper (U Bielefeld)

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20.07.2023

17 Uhr s.t.

 

Kai Cui (TU Darmstadt)

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Interessenten sind herzlich eingeladen.

 

 

 

Für Rückfragen wenden Sie sich bitte an:

Frau Sabine Bergmann

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