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PRODID:-//Memento EPFL//
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SUMMARY:An optimal transport problem with backward martingale constraints 
 motivated by insider trading.
DTSTART:20210219T140000
DTEND:20210219T153000
DTSTAMP:20260407T215708Z
UID:bf16582c8cb08460009435fb2934dc166e7623b6c0cb60bd978df3a1
CATEGORIES:Conferences - Seminars
DESCRIPTION:Dmitry KRAMKOV\, Carnegie Mellon Uni.\nGiven a probability mea
 sure ν on R2\, we want to minimize\nc(x\, y)dγ over γ ∈ Γ(ν)\nfor t
 he covariance-type cost function c(x\, y) = (y1 −x1)(y2 −x2)\, where 
 Γ(ν) is the family of probability measure γ on R2 × R2\, that have ν 
 as their y-marginal and make a martingale from the canonical two-dimension
 al process (x\, y). Problem (1) belongs to the class of optimal transport 
 problems with backward martingale constraints\, in the sense that the init
 ial x-marginal is part of the solution. The motivation comes from a versio
 n of Kyle’s equilibrium with insider.\nOur main result states that a pro
 bability measure γ ∈ Γ(ν) is optimal if and only if there is a maxima
 l monotone set G ⊂ R2 such that (1) it supports the x-marginal of γ\, a
 nd (2) c(x\, y) = minz∈G c(z\, y) for every (x\, y) ∈ supp γ. Further
 more\, if ν is continuous\, then the solution is uniquely determined by t
 he subdifferential of the concave function uG(y) = infz∈G{c(z\, y) − 
 y1y2}.\n\nThe presentation is based on a joint paper with Yan Xu available
  on\nPaper: https://arxiv.org/abs/1906.03309.
LOCATION:Zoom
STATUS:CONFIRMED
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