Stochastic Analysis & Mathematical Finance Seminars

Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

Past events in this series

I will present recent results on the statistical behaviour of a large number of weakly interacting diffusion processes evolving under the influence of a periodic interaction potential. We study the combined mean field and diffusive (homogenisation) limits. In particular, we show that these two limits do not commute if the mean field system constrained on the torus undergoes a phase transition, i.e., if it admits more than one steady state. A typical example of such a system on the torus is given by mean field plane rotator (XY, Heisenberg, O(2)) model. As a by-product of our main results, we also analyse the energetic consequences of the central limit theorem for fluctuations around the mean field limit and derive optimal rates of convergence in relative entropy of the Gibbs measure to the (unique) limit of the mean field energy below the critical temperature. This is joint work with Matias Delgadino (U Texas Austin) and Rishabh Gvalani (MPI Leipzig).



  • Stochastic Analysis & Mathematical Finance Seminars
25 October 2021

Given a point and a loop in the plane, one can define a relative integer which counts how many times the curve winds around the point. We will discuss how this winding function, defined for almost every points in the plane, allows to define some integrals along the loop. Then, we will investigate some properties of it when the loop is Brownian.
In particular, we will explain how to recover data such as the Lévy area of the curve and its occupation measure, based on the values of the winding of uniformly distributed points on the plane.


  • Stochastic Analysis & Mathematical Finance Seminars
8 November 2021

Classical approaches to optimal portfolio selection problems are based 
on probabilistic models for the asset returns or prices. However, by 
now it is well observed that the performance of optimal portfolios are 
highly sensitive to model misspecifications. To account for various 
type of model risk, robust and model-free approaches have gained more 
and more importance in portfolio theory. Based on a rough path 
foundation, we develop a model-free approach to stochastic portfolio 
theory and Cover's universal portfolio. The use of rough path theory 
allows treating significantly more general portfolios in a model-free 
setting, compared to previous model-free approaches. Without the 
assumption of any underlying probabilistic model, we present pathwise 
Master formulae analogously to the classical ones in stochastic 
portfolio theory, describing the growth of wealth processes generated 
by pathwise portfolios relative to the wealth process of the market 
portfolio, and we show that the appropriately scaled asymptotic growth 
rate of Cover's universal portfolio is equal to the one of the best 
retrospectively chosen portfolio. The talk is based on joint work with 
Andrew Allan, Christa Cuchiero and Chong Liu.


  • Stochastic Analysis & Mathematical Finance Seminars
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