Probability Colloqium
Date
Time
16:oo
Location:
HUB; RUD 25; 1.115
Hendrik Weber (Münster)

tba

Mathematical Finance Seminar
Date
Time
17:oo
Location:
HUB; RUD 25; 1.115
David Criens (Freiburg)

Nonlinear Diffusions and their Feller Properties

Motivated by Knightian uncertainty, S. Peng introduced his celebrated G–Brownian motion. Intuitively speaking, it corresponds to a dynamic worst case expectation in a model where volatility is uncertain but postulated to take values in a bounded interval. Natural extensions of the G–Brownian motion are nonlinear diffusions, whose volatility (and drift) takes values in a random set that is allowed to depend on the canonical process in a Markovian way. Nonlinear diffusions satisfy the dynamic programming principle, which entails the semigroup property of a corresponding family of sublinear operators. In this talk, we discuss regularity properties of these semigroups that allow us to relate them to evolution equations. In particular, we explain a novel type of smoothing property and a stochastic representation result for general sublinear semigroups with pointwise generators of Hamilton-Jacobi-Bellman type. Latter also implies a unique characterization theorem for such semigroups.

The talk is based on joint work with Lars Niemann (University of Freiburg).

Mathematical Finance Seminar
Date
Time
16:oo
Location:
HUB; RUD 25; 1.115
Christoph Czichowski (London)

Numeraire-invariance and the law of one price in mean-variance portfolio selection and quadratic hedging

Probability Colloqium
Date
Time
16:15
Location:
HUB; RUD 25; 1.115
Mathias Beiglböck (U Vienna)

Martingale Benamou-Brenier

In classical optimal transport, the contributions of Benamou-Brenier and Mc- Cann regarding the time-dependent version of the problem are cornerstones of the field and form the basis for a variety of applications in other mathematical areas.

Stretched Brownian motion provides an analogue for the martingale version of this problem. We provide a characterization in terms of gradients of convex functions, similar to the characterization of optimizers in the classical transport problem for quadratic distance cost.

Based on joint work with Julio Backhoff-Veraguas, Walter Schachermayer and Bertram Tschiderer.

Mathematical Finance Seminar
Date
Time
17:oo
Location:
HUB; RUD 25; 1.115
Leandro Sanchez-Betancourt (Oxford)

tba

Mathematical Finance Seminar
Date
Time
16:oo
Location:
HUB; RUD 25; 1.115
John Schoenmakers (WIAS)

tba

Probability Colloqium
Date
Time
16:oo
Location:
HUB; RUD 25; 1.115
Peter Nejjar (U. Potsdam)

tba

Probability Colloqium
Date
Time
Location:
17:oo
Pierre-François Rodriguez (IC London)

tba

Probability Colloqium
Date
Time
16:oo
Location:
HUB; RUD 25; 1.115
Hendrik Weber (U. Münster)

(CANCELLED)

Probability Colloqium
Date
Time
17:15
Location:
HUB, RUD 25; 1.115
Michael Scheutzow (TU Berlin)

Stability and instability of a planar random dynamical system

We study a planar stochastic differential equation with additive noise for which the rotational speed is of the form ρ(R) where R is the radial part.

We investigate how phenomena like strong or weak synchronization, existence of a pullback or a point attractor and strong completeness of the associated random dynamical system depend on the function ρ. This is joint work (in progress) with Maximilian Engel and Dennis Chemnitz (FU Berlin).