Infinite regularization by noise

Abstract:  It is a classical yet surprising result that noise can have a regularizing effect on differential equations. For example, adding a Brownian motion to an ODE with a bounded and measurable vector field leads to a well-posed equation with Lipschitz continuous flow. While the equation without noise may have none or many solutions. Classical proofsare

Numerical schemes for radial Dunkl processes

Abstract:  In this talk, we consider the numerical approximation for a class of radial Dunkl processes corresponding to arbitrary (reduced) root systems. This class contains some well-known processes such as Bessel processes and Dyson’s Brownian motions. We introduce a backward and truncated Euler–Maruyama scheme, which can be implemented on a computer, and study its rate of

Back to the future: Using full genome data to infer past species history and ecological/life-history traits

Speaker: Prof. Aurélien Tellier (Professor of population genetics, Technical University of Munich, Germany) Abstract:  The field of evolutionary genetics is profoundly rooted in stochastic mathematical theory and since several years the theory has been extended to model the evolution of full genomes. Indeed, large amounts of full genome data are becoming available for human but also non-model organisms.

Davie type estimations for the Brownian sheet

Abstract: We prove and apply a local time-space integration formula to provide several Davie type bounds for the Brownian sheet. This local time-space integration formula is similar to that obtained by Eisenbaum for the reversible semimartingales. Davie type bounds are useful to prove strong uniqueness results for stochastic differential equations with irregular drifts. Such estimates originated

On “rough” Quadratic Wiener Functionals

Speaker: Prof. Jiro Akahori (Professor, Department of Mathematical Sciences, Ritsumeikan University, Japan) Abstract: In this talk, the law of functionals of fractional Brownian motion, which is quadratic in an infinite-dimensional sense, and also related topics, will be discussed.  We are interested in how the classical results on quadratic functionals of standard Browian motion are generalized. Applications will

Hyperbolic Conservation Laws arising in the study of the forward-forward Mean-Field Games.

Speaker: Prof. Marc Sedjro (German Research Chair, AIMS South Africa) Abstract: In this talk, we introduce several models of the so-called forward-forward Mean-Field Games (MFGs). The forward-forward models arise in the study of numerical schemes to approximate stationary MFGs. We establish a link between these models and a class of hyperbolic conservation laws. Furthermore, we investigate the

Functional Limit Theorems for Irregular Stochastic Processes

Speaker: Prof. Dr. Stefan Ankirchner (Professor of Stochastic Analysis, Institute of Mathematics, Friedrich-Schiller-University, Germany) Abstract: In this talk we will see that every one-dimensional continuous regular strong Markov process can be approximated with coin tossing Markov chains. In particular, it is possible to approximate an SDE with an irregular diffusion coefficient with such Markov chains. We also discuss the numerical approximation

Pricing and hedging of options in non-linear incomplete financial market models

Abstract: We will study the superhedging price (and superhedging strategies) of European and American options in non-linear incomplete market models with default, with a particular focus on the case of the American options which is more involved. We will provide a dual representation of the seller’s (superhedging) price for the American option in terms of

Speaker: Prof. Said Hamadene (LMM, Le Mans University, France)

Abstract: In this talk, we study a class of reflected backward stochastic differential equations (BSDEs) of mean-field type, where the mean-field interaction in terms of the expected value E[Y ] of the Y-component of the solution enters both the driver and the lower obstacle. We consider the case where the lower obstacle is a deterministic

Speaker:Prof. (Emeritus) Bernt Øksendal (University of Oslo, Norway)

Abstract: We study option prices in financial markets where the risky asset prices are modelled by jump diffusions. For simplicity, we put the risk-free asset price equal to 1. Such markets are typically incomplete, and therefore there are in general infinitely many arbitrage-free option prices in these markets. We consider in particular European options with