Past Mathematical Finance Internal Seminar

20 October 2017
13:00
Christoph Siebenbrunner and Andreas Sojmark
Abstract

Christoph Siebenbrunner:

Clearing Algorithms and Network Centrality

I show that the solution of a standard clearing model commonly used in contagion analyses for financial systems can be expressed as a specific form of a generalized Katz centrality measure under conditions that correspond to a system-wide shock. This result provides a formal explanation for earlier empirical results which showed that Katz-type centrality measures are closely related to contagiousness. It also allows assessing the assumptions that one is making when using such centrality measures as systemic risk indicators. I conclude that these assumptions should be considered too strong and that, from a theoretical perspective, clearing models should be given preference over centrality measures in systemic risk analyses.


Andreas Sojmark:

An SPDE Model for Systemic Risk with Default Contagion

In this talk, I will present a structural model for systemic risk, phrased as an interacting particle system for $N$ financial institutions, where each institution is removed upon default and this has a contagious effect on the rest of the system. Moreover, the financial instituions display herding behavior and they are exposed to correlated noise, which turns out to be an important driver of the contagion mechanism. Ultimately, the motivation is to provide a clearer connection between the insights from dynamic mean field models and the detailed study of contagion in the (mostly static) network-based literature. Mathematically, we prove a propagation of chaos type result for the large population limit, where the limiting object is characterized as the unique solution to a nonlinear SPDE on the positive half-line with Dirichlet boundary. This is based on joint work with Ben Hambly and I will also point out some interesting future directions, which are part of ongoing work with Sean Ledger.

  • Mathematical Finance Internal Seminar
9 June 2017
13:00
Pietro Siorpaes
Abstract


Martingale optimal transport is a variant of the classical optimal transport problem where a martingale constraint is imposed on the coupling. In a recent paper, Beiglböck, Nutz and Touzi show that in dimension one there is no duality gap and that the dual problem admits an optimizer. A key step towards this achievement is the characterization of the polar sets of the family of all martingale couplings. Here we aim to extend this characterization to arbitrary finite dimension through a deeper study of the convex order

 

  • Mathematical Finance Internal Seminar

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