Date/Time
Date(s) - 12/01/2024
11:00 am - 12:00 pm

Friday’s first Phi-Mac seminar of the term:

Date/ Time: Jan 12, 2024 at 11:00am (Toronto time)

Venue: Zoom via the following link:

Join Zoom Meeting https://mcmaster.zoom.us/j/99871779472
Meeting ID: 998 7177 9472

Speaker: David Prömel (University of Mannheim)

Title: Pathwise integration for robust finance

Abstract: In the analysis of the financial crises 2007-2008, risk caused by financial modelling was identified as one of the main challenges. To treat the issue of model risk, more robust approaches in mathematical finance emerged in the past decades, like mathematical finance under Knightian uncertainty and model-free finance in continuous time. For these robust approaches, sophisticated pathwise “stochastic” integration is fundamental and inevitable. In this talk, we discuss two pathwise integration theories suitable for robust finance in continuous time. First, based on Vovk’s super-hedging approach to model-free financial mathematics, we show the existence of quadratic variation and develop a model-free Itô integration for “typical price paths”. Secondly, using rough path theory, we provide an entirely deterministic foundation for stochastic Itô integration, which covers the most commonly applied trading strategies. Applications to pathwise portfolio theory and first-order Euler schemes are
discussed.