From Bachelier to Dupire via optimal transport

Famously, mathematical finance was started by Bachelier in his 1900 PhD thesis where – among many other achievements – he also provided a formal derivation of the Kolmogorov forward equation. This also forms the basis for Dupire’s (again formal) solution to the problem of finding an arbitrage-free model calibrated to a given volatility surface. The latter result has rigorous counterparts in the theorems of Kellerer and Lowther. In this survey article, we revisit these hallmarks of stochastic finance, highlighting the role played by some optimal transport results in this context.

A Calculus of Tracking: Theory and Practice

Online tracking techniques, the interactions among trackers, and the economic and social impact of these procedures in the advertising ecosystem have received increasing attention in the last years. This work proposes a novel formal model that describes the foundations on which the visible process of data sharing behaves in terms of the network configurations of the Internet (included CDNs, shared cookies, etc.). From our model, we define relations that can be used to evaluate the impact of different privacy mitigations and determine if websites should comply with privacy regulations. We show that the calculus, based on a fragment of intuitionistic logic, is tractable and constructive: any formal derivation in the model corresponds to an actual tracking practice that can be implemented given the current configuration of the Internet. We apply our model on a dataset obtained from OpenWPM to evaluate the effectiveness of tracking mitigations up to Alexa Top 100.