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2019

Compactness in Adapted Weak Topologies

Eder, Manu

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Over the years a number of topologies for the set of laws of stochastic processes have been proposed.

Building on the weak topology they all aim to capture more accurately the temporal structure of the processes.
In a parallel paper we show that all of these topologies (i.e.
the information topology of Hellwig, the nested distance topology of Pflug-Pichler, the extended weak convergence of Aldous and a topology built from Lasalle's notion of a causal transference plan) are equal in finite discrete time.

Compactness in Adapted Weak Topologies · Around

Built on

Weak convergence and general theory of processes
D. J. Aldous · 1981
Earlier work this paper cites.
Topics in propagation of chaos
A.-S. Sznitman · 1991
Earlier work this paper cites.
Sequential decisions under uncertainty and the maximum theorem
M. F. Hellwig · 1996
Earlier work this paper cites.
Optimal Transport. Old and New
C. Villani · 2009
Earlier work this paper cites.
A distance for multistage stochastic optimization models
G. C. Pflug and A. Pichler · 2012
Earlier work this paper cites.

Similar

Evaluations of risk measures for different probability measures
A. Pichler · 2013
Cited alongside, same era.
The topology of information on the space of probability measures over Polish spaces
M. Barbie and A. Gupta · 2014
Cited alongside, same era.
Multistage stochastic optimization
G. C. Pflug and A. Pichler · 2014
Cited alongside, same era.
Dynamic generation of scenario trees
G. C. Pflug and A. Pichler · 2015
Cited alongside, same era.
From empirical observations to tree models for stochastic optimization: convergence properties
G. C. Pflug and A. Pichler · 2016
Cited alongside, same era.

Then

Incorporating statistical model error into the calculation of acceptability prices of contingent claims
Original
M. Glanzer, G. C. Pflug, and A. Pichler · 2017
Later among the works it cites.
Existence, Duality, and Cyclical monotonicity for weak transport costs
Original
J. Backhoff Veraguas, M. Beiglböck, and G. Pammer · 2018
Later among the works it cites.
Causal transference plans and their Monge-Kantorovich problems
R. Lassalle · 2018
Later among the works it cites.
All Adapted Topologies are Equal
Original
J. Backhoff-Veraguas, D. Bartl, M. Beiglböck, and M. Eder · 2019
Closest in time.
Stability of martingale optimal transport and weak optimal transport
Original
J. Backhoff-Veraguas and G. Pammer · 2019

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