Monge–Kantorovich Mass Transference Problem, Minimal Distances and Minimal Norms

Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov and Frank J. Fabozzi
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Svetlozar T. Rachev: Stony Brook University, Department of Applied Mathematics and Statistics College of Business
Lev B. Klebanov: Charles University, Department of Probability and Statistics
Stoyan V. Stoyanov: EDHEC Business School EDHEC-Risk Institute
Frank J. Fabozzi: EDHEC Business School EDHEC-Risk Institute

Chapter Chapter 5 in The Methods of Distances in the Theory of Probability and Statistics, 2013, pp 109-143 from Springer

Abstract: Abstract The goals of this chapter are to: Introduce the Kantorovich and Kantorovich–Rubinstein problems in one-dimensional and multidimensional settings; Provide examples illustrating applications of the abstract problems; Provide examples illustrating applications of the abstract problems; Discuss the multivariate Kantorovich and Kantorovich–Rubinstein theorems, which provide dual representations of certain types of minimal distances and norms; Discuss a particular application leading to an explicit representation for a class of minimal norms.

Keywords: Cost Function; Dual Representation; Transportation Problem; Minimal Norm; Borel Probability Measure (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-4869-3_5

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DOI: 10.1007/978-1-4614-4869-3_5

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