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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


 
Ort: HU Berlin,
Institut für Mathematik,
Rudower Chaussee 25, 12489 Berlin
Raum 1.115
 
Zeit: Donnerstag, 16 Uhr/17 Uhr c.t.
 

 

 

24.10.2019

(16 Uhr c.t.)

Jan Kallsen  (Universität Kiel)

Should I invest in the market portfolio?

 

Abstract: Guided by stylised facts and inspired by Robert Fernholz' stochastic portfolio theory, we present a parsimonious stationary diffusion model for the entire stock market. Its ultimate purpose is to decide whether there is a simple more efficient alternative to the market portfolio. At this stage we discuss the qualitative implications of the model. A crucial role is played by the speed measure and by the local time at the boundary of the support of the diffusion process under consideration.

24.10.2019

(17 Uhr c.t.)

N.N.

tba

 

Abstract: 

07.11.2019

(16 Uhr c.t.)

 

 

Sara Svaluto-Ferro (University of Vienna)

Polynomial processes - a universal modeling class

 

Abstract: We introduce polynomial jump-diffusions taking values in an arbitrary Banach space via their infinitesimal generator. We obtain two representations of the (conditional) moments in terms of solution of systems of ODEs. We illustrate the wide applicability of these formulas by analyzing several state spaces. We start by the finite dimensional setting, where we recover the well-known moment formulas. We then study the probability-measure valued setting, where we also obtain an existence result for the corresponding martingale problems. Moving to more recent results, we consider (potentially rough) forward variance polynomial models and we illustrate how to use the moment formulas to compute prices of VIX options. Finally, we show that the signature process of a d-dimensional Brownian motion is polynomial and derive its expected value via the polynomial approach. This is in fact just an illustrative example: the same applies to solutions of every SDE with analytic coefficients.

07.11.2019

(17 Uhr c.t.)

 

 

Julio Backhoff (University of Twente)

The Mean Field Schrödinger Problem

 

Abstract: I will introduce the mean field Schrödinger problem, concerned with finding the most likely evolution of a cloud of interacting Brownian particles conditionally on their initial and final configurations. New energy dissipation estimates are shown, yielding exponential convergence to equilibrium as the time between initial and final observations grows to
infinity. The method reveals novel functional inequalities involving the mean field entropic cost, as well as an interesting connection with the theory of PDEs. (Joint work with Giovani Conforti, Ivan Gentil and Christian Léonard.) 

21.11.2019 

(16 Uhr c.t.)

 

Stefan Gerhold (Technische Universität Wien) 

Dynamic trading under integer constraints

 

Abstract: We first review results on arbitrage theory for some notions of "simple" strategies, which do not allow continuous portfolio rebalancing by  arbitrary amounts. Then, the focus of the talk is on trading under integer constraints, that is, we assume that the offered goods or shares are traded in integer quantities instead of the usual real quantity assumption. For finite probability spaces and rational asset prices this has little effect on the core of the theory of no-arbitrage pricing. For price processes not restricted to the rational numbers, a novel theory of integer arbitrage free pricing and hedging emerges. We establish an FTAP, involving a set of absolutely continuous martingale measures satisfying an additional property. The set of prices of a contingent claim is not necessarily an interval, but is either empty or dense in an interval. We also discuss superhedging with integral portfolios.

Joint work with Paul Eisenberg.

21.11.2019

(17 Uhr c.t.)

 

Tiziano De Angelis (University of Leeds)

Some Explicit Results on Dynkin Games with Incomplete and Asymmetric Information

 

Abstract: 

In this talk I will consider two types of Dynkin game with non-standard information structures. The first one is a zero-sum game between two players who observe a geometric Brownian motion but in which the minimiser knows the drift of the process whereas the maximiser doesn't know it. We construct an explicit Nash equilibrium in which the uninformed player uses a pure strategy and the informed player uses a randomised strategy. The second game is a non-zero sum game between two agents interested in the purchase of the same asset. Neither of the two players knows with certainty whether their competitor is `active' and in that sense that they have uncertain competition. Also in this case we construct explicitly a Nash equilibrium in which both players randomise their strategy.

 

05.12.2019

(16 Uhr c.t.)

 

 

N.N.

tba

 

Abstract: 

05.12.2019

(17 Uhr c.t.)

 

Frank Seifried (Universität Trier)

tba

 

Abstract: 

09.01.2020

(16 Uhr c.t.)

 

N.N. 

tba

 

Abstract: 

09.01.2020

(17 Uhr c.t.)

 

N.N. 

tba

 

Abstract: 

23.01.2020

(16 Uhr c.t.)

 

Peter Tankov (Université Paris-Saclay)

tba

 

Abstract: 

23.01.2020

(17 Uhr c.t.)

 

Patrick Cheridito (ETH Zürich)

tba

 

Abstract: 

06.02.2020

(16 Uhr c.t.)

 

N.N. 

tba

 

Abstract: 

06.02.2020

(17 Uhr c.t.)

 

Thibaut Mastrolia (CMAP, Ecole Polytechnique, Palaiseau)

tba

 

Abstract: 

Interessenten sind herzlich eingeladen.

 

 

 


Für Rückfragen wenden Sie sich bitte an:

Frau Sabine Bergmann
bergmann@mathematik.hu-berlin.de
Telefon: 2093 5811
Telefax: 2093 5848

Verweise
Stochastik