Mathematical Finance Seminar
Date
Time
16:oo
Location:
HUB; RUD 25; 1.115
Philipp Jettkant (University of Oxford)

On two Formulations of McKean–Vlasov Control with Killing

We study a McKean–Vlasov control problem with killing and common noise. The particles in this control model live on the real line and are killed at a positive intensity whenever they are in the negative half-line. Accordingly, the interaction between particles occurs through the subprobability distribution of the living particles. We establish the existence of an optimal semiclosed-loop control that only depends on the particles’ location and not their cumulative intensity. This problem cannot be addressed through classical mimicking arguments, because the particles’ subprobability distribution cannot be reconstructed from their location alone. Instead, we represent optimal controls in terms of the solutions to semilinear BSPDEs and show those solutions do not depend on the intensity variable.

Probability Colloqium
Date
Time
17:oo
Location:
HUB; RUD 25; 1.115
Jessica Lin (Montréal)

Generalized Front Propagation for Stochastic Spatial Models

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