Peacocks and Associated Martingales, with Explicit Constructions

By F. Hirsch. 2011

117 citations recorded by the source corpus.

Subfields: Demography, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/3eb5e22c4720f98dcb8381711234685bdb298458

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Citations in the corpus

Characterization of a class of weak transport-entropy inequalities on the line (2015, background): “We refer the interested reader to [27] and [23] for further results and bibliographic references.”
Optimal transport and Skorokhod embedding (2013, methodology): “[29], who have used solutions to the Skorokhod embedding problem to construct Peacocks; and Gassiat et.”
Some Properties of the Kilbas-Saigo Function (2020, unknown): “x Lα for every 0 ≤ α≤ β≤ 1.Applying the deﬁnition of convex ordering to the function ϕ(x) = ex,we get Lβ(x) ≤ Lα(x) for every x<0 and 0 ≤ α≤ β≤ 1,as required. Remark 5.5. (a) In the terminology of [11], the family {L1−α, α∈ [0,1]} is a peacock, whose associated multiplicative martingale is comple”
An Explicit Martingale Version of the One-Dimensional Brenier's Theorem with Full Marginals Constraint (2016, unknown): “Given a continuous family of marginal distributions which is non-decreasing in convex ordering, a stochastic process calibrated to all the marginals is called a peacock (or PCOC “Processus Croissant pour l’Ordre Convexe” in French) in Hirsch, Profeta, Roynette & Yor [43].”
On a problem of optimal transport under marginal martingale constraints (2012, background): “For the first property, see [12], Exercise 1.”
Optimal Skorokhod embedding given full marginals and Azema-Yor peacocks (2015, background): “Speciﬁcally, Madan and Yor [25] provide, under certain assumptions, a characterization of the continuous time martingale obtained from the Az´ema-Yor embedding.”
Martingale Benamou–Brenier: A probabilistic perspective (2017, background): “In contemporary terms (see [40]), (μt)t∈R+ is called a peacock and (Xt)t∈R+ is a Markovian martingale associated to this peacock.”
On a mixture of Brenier and Strassen Theorems (2018, methodology): “See the monograph [37] on peacocks, [39, 51] for the approach by Lowther and [10, 38, 44] for extensions.”