Interacting particles and market capitalization curves

26.01.2023 16:00 - 17:00

Florian Huber (University of Vienna)

Abstract: Motivated by the robustness of the so-called market capitalization curve, our goal is to study the behaviour of equity market models on a macroscopic scale. This is done by extending the volatility stabilized market models studied by Fernholz and co-authors and allowing for simple correlation structure induced by a common noise term. Letting the number of companies approach infinity, we show that the limit of the empirical measure of the N-company system converges to the unique solution of a degenerate, non-linear SPDE. The obtained limit also possess a representation as a conditional probability of the solution to a certain McKean-Vlasov SDE.
This is joint work in progress with Christa Cuchiero.

WU Vienna, Welthandelsplatz 1, 1020 Wien, ground floor, SR D4.0.039