4 citations · 14 across the 12 of their papers we have counts for
13 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 ord…
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…
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…
Multidimensional specific relative entropy between continuous martingales
Julio Backhoff, Edoardo Kimani Bellotto
In continuous time, the laws of martingales tend to be singular to each other. Notably, N. Gantert introduced the concept of specific relative entropy between real-valued continuou…
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}…
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…
Stochastic Gradient Descent for Barycenters in Wasserstein Space
Julio Backhoff-Veraguas, Joaquin Fontbona, Gonzalo Rios +1
We present and study a novel algorithm for the computation of 2-Wasserstein population barycenters of absolutely continuous probability measures on Euclidean space. The proposed me…
Estimating processes in adapted Wasserstein distance
Julio Backhoff, Daniel Bartl, Mathias Beiglböck +1
A number of researchers have independently introduced topologies on the set of laws of stochastic processes that extend the usual weak topology. Depending on the respective scienti…
The mean field Schrödinger problem: ergodic behavior, entropy estimates and functional inequalities
Julio Backhoff-Veraguas, Giovani Conforti, Ivan Gentil +1
We study the mean field Schrödinger problem (MFSP), that is the problem of finding the most likely evolution of a cloud of interacting Brownian particles conditionally on the obser…
Causal transport in discrete time and applications
Julio Backhoff Veraguas, Mathias Beiglböck, Yiqing Lin +1
Loosely speaking, causal transport plans are a relaxation of adapted processes in the same sense as Kantorovich transport plans extend Monge-type transport maps. The corresponding…
Conditional Analysis and a Principal-Agent problem
Julio Backhoff, Ulrich Horst
We analyze conditional optimization problems arising in discrete time Principal-Agent problems of delegated portfolio optimization with linear contracts. Applying tools from Condit…
Some sensitivity results in stochastic optimal control: A Lagrange multiplier point of view
Julio Backhoff, Francisco Silva
In this work we provide a first order sensitivity analysis of some parameterized stochastic optimal control problems. The parameters can be given by random processes. The main tool…