I am mostly interested in the interface between Applied Probability Theory, Stochastic Optimization and Optimal Transport, with applications (mainly) in Finance, Economics and Data Science.
My current work deals with:
Constrained optimal transport (e.g. martingale and causal optimal transport) as a theoretical tool and as a modeling paradigm in finance, economics, and statistics.
Stochastic optimal control, convex analysis and optimal transport, as tools to uncover new phenomena and construct new objects in probability theory and stochastic analysis.
A sample of my current projects:
Causal Wasserstein distances in mathematical finance
The geometry of stochastic processes
Metric projection of an 'idealized' process onto a set of processes that are 'calibrated-to-data'
Specific relative entropy between continuous martingales and its applications