DFG-Research Centre "Mathematics for key technologies - MATHEON": Probabilistic Interaction Models for the Microstructure of Asset Price Fluctuation (TP E 3)

In the standard economic paradigm, asset prices are determined by the markets view of their fundamental values. But there is usually no rigorous modeling of the interactions which lead to such an aggregate assessment. In the standard models of Mathematical Finance, the fluctuation of asset prices is simply given as a stochastic process, and the analysis of hedging and investment strategies starts from there. There is, however, an increasing awareness that this approach fails to capture some crucial sources of financial risk. One such source is the impact of interactive shifts in investor sentiment on asset prices which may generate a considerable liquidity risk. In order to analyze such effects in a more rigorous manner, one needs mathematical models for the microstructure of financial markets.