Mathematical aspects of market impact-modeling

• Applicant: Professor Dr. Alexander Schied
• Subject Area: Mathematics
• Term: from 2010 to 2017
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 179751998

Market impact models provide a dynamic and quantitative description of the feedback of trades on the underlying price process. The mathematical analysis of such models is of interest from several perspectives. First, the nonlinearities arising from the feedback of strategies can create novel and unexpected effects, which make market impact models an interesting and rewarding research subject from a mathematical point of view. Second, from the point of view of applications, it would be desirable to gain a better understanding of market impact models and their behavior. Third, market impact is one of the basic mechanisms responsible for price formation, and so its analysis might contribute to new insights on how financial markets function. In the first funding period of the project we have in particular investigated the viability of market impact models. During the second funding period we will, on the one hand, focus on further investigating the connection between superprocesses and stochastic optimal control in market impact models. On the other hand, we will analyze market impact games in which several competitors interact through the price impact generated by their strategies.

• DFG Programme: Research Grants