6 papers
Analytical Approach to Continuous-Time Causal Optimal Transport
Julio Backhoff, Erhan Bayraktar, Ibrahim Ekren +1
We study causal optimal transport in continuous time, with Markovian cost, between a finite-state Markov source and a diffusion target. By replacing the source with its conditional…
Bridging classical and martingale Schrödinger bridges
Julio Backhoff, Mathias Beiglböck, Giorgia Bifronte +1
We investigate the martingale Schrödinger bridge, recently introduced by Nutz and Wiesel as a distinguished martingale transport plan between two probability measures in convex or…
Reciprocal Specific Relative Entropy between Continuous Martingales
Julio Backhoff, Xin Zhang
We introduce a novel notion of divergence between continuous martingales; the reciprocal specific relative entropy. First, we motivate this definition from multiple perspectives. T…
The geometry of financial institutions -- Wasserstein clustering of financial data
Lorenz Riess, Mathias Beiglböck, Johannes Temme +2
The increasing availability of granular and big data on various objects of interest has made it necessary to develop methods for condensing this information into a representative a…
Geometric Martingale Benamou-Brenier transport and geometric Bass martingales
Julio Backhoff, Gregoire Loeper, Jan Obloj
We introduce and study geometric Bass martingales. Bass martingales were introduced in \cite{Ba83} and studied recently in a series of works, including \cite{BaBeHuKa20,BaBeScTs23}…
Exciting games and Monge-Ampère equations
Julio Backhoff, Zhizhang Wang, Xin Zhang
We consider a competition between players, and aim to identify the "most exciting game'' of this kind. This is translated, mathematically, into a stochastic optimization prob…