A basic problem when trading in financial markets is to analyze the price movement caused by placing an order. Clearly we expect - ceteris paribus - that placing an order will move the price to the disadvantage of the agent. This price movement is called the market impact. Following the recent work of A. Kyle and A. Obizhaeva we apply dimensional analysis - a line of arguments well known in classical physics - to analyze to which extent the square root law applies. This universal law claims that the market impact is proportional to the square root of the size of the order. We also analyze the dependence of the trading activity on a stock, i.e. number of trades per unit of time, in dependence of some suitable explanatory variables. Dimensional analysis leads to a 2/3 law: the number of trades is proportional to the power 2/3 of the exchanged risk. The mathematical tools of this analysis reside on elementary linear algebra. Joint work with Mathias Pohl, Alexander Ristig and Ludovic Tangpi.
Walter Scachermayer is a professor at the mathematical faculty of the University of Vienna. He received the Wittgenstein Prize in 1998 and is a member of the Leopoldina. His other honors include an honorary doctorate from the University of Paris-Dauphine in 2011, the Vienna City of Science Prize, and the membership of Academia Europaea.