Weitere Informationen zum ausgewählten Kolloquiumsvortrag:

On Absence of Arbitrage and Propagation of Chaos

Dr. David Criens

Tuesday, 2022-01-18 10:30

In the talk I discuss two recent research projects. The first part is related to mathematical finance. More precisely, I consider a single asset model whose (discounted) price process is assumed to be a non-negative semimartingale diffusion. The important new feature of this model is that the diffusion is not assumed to have an SDE representation, which allows possible local time effects such as sticky points. For this financial model I discuss explicit deterministic sufficient and necessary conditions for the existence and absence of arbitrage in the sense of NFLVR. The proof of the result is based on the concept of separating times, which I also shortly explain. In the second part of my talk I discuss a propagation of chaos result for a system of (weakly) interacting stochastic PDEs. More precisely, under quite mild continuity and linear growth conditions, I present a law of large numbers and the corresponding McKean-Vlasov limit. The first part of my talk is based on joint work with Mikhail Urusov (U Duisburg-Essen).