Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a problem of optimal transport under marginal martingale constraints   The basic problem of optimal transportation consists in minimizing the
expected costs $\mathbb {E}[c(X_1,X_2)]$ by varying the joint distribution
$(X_1,X_2)$ where the marginal distributions of the random variables $X_1$ and
$X_2$ are fixed. Inspired by recent applications in mathematical finance and
connections with the peacock problem, we study this problem under the
additional condition that $(X_i)_{i=1,2}$ is a martingale, that is, $\mathbb
{E}[X_2|X_1]=X_1$. We establish a variational principle for this problem which
enables us to determine optimal martingale transport plans for specific cost
functions. In particular, we identify a martingale coupling that resembles the
classic monotone quantile coupling in several respects. In analogy with the
celebrated theorem of Brenier, the following behavior can be observed: If the
initial distribution is continuous, then this "monotone martingale" is
supported by the graphs of two functions $T_1,T_2:\mathbb {R}\to \mathbb {R}$.

11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph