Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The potential of the shadow measure   It is well known that given two probability measures $\mu$ and $\nu$ on
$\mathbb{R}$ in convex order there exists a discrete-time martingale with these
marginals. Several solutions are known (for example from the literature on the
Skorokhod embedding problem in Brownian motion). But, if we add a requirement
that the martingale should minimise the expected value of some functional of
its starting and finishing positions then the problem becomes more difficult.
Beiglb\"{o}ck and Juillet (Ann. Probab. 44 (2016) 42-106) introduced the shadow
measure which induces a family of martingale couplings, and solves the optimal
martingale transport problem for a class of bivariate objective functions. In
this article we extend their (existence and uniqueness) results by providing an
explicit construction of the shadow measure and, as an application, give a
simple proof of its associativity.

21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph