A separating hyperplane theorem, the fundamental theorem of asset pricing, and Markov's principle

Research output: Contribution to journal › Article › Research › peer review

Authors

  • Josef Berger
  • G. Svindland

External Research Organisations

  • Ludwig-Maximilians-Universität München (LMU)
View graph of relations

Details

Original languageEnglish
Pages (from-to)1161-1170
Number of pages10
JournalAnnals of pure and applied logic
Volume167
Issue number11
Publication statusPublished - 1 Nov 2016
Externally publishedYes

Abstract

We prove constructively that every uniformly continuous convex function f:X→R + has positive infimum, where X is the convex hull of finitely many vectors. Using this result, we prove that a separating hyperplane theorem, the fundamental theorem of asset pricing, and Markov's principle are constructively equivalent. This is the first time that important theorems are classified into Markov's principle within constructive reverse mathematics.

Keywords

    Constructive mathematics, Markov's principle, Reverse mathematics, Separating hyperplane theorem, The fundamental theorem of asset pricing

ASJC Scopus subject areas

Cite this

A separating hyperplane theorem, the fundamental theorem of asset pricing, and Markov's principle. / Berger, Josef; Svindland, G.
In: Annals of pure and applied logic, Vol. 167, No. 11, 01.11.2016, p. 1161-1170.

Research output: Contribution to journal › Article › Research › peer review

Berger J, Svindland G. A separating hyperplane theorem, the fundamental theorem of asset pricing, and Markov's principle. Annals of pure and applied logic. 2016 Nov 1;167(11):1161-1170. doi: 10.1016/j.apal.2016.05.003
Download
@article{404f30d66f1e447cbb67a722a65b4af8,
title = "A separating hyperplane theorem, the fundamental theorem of asset pricing, and Markov's principle",
abstract = "We prove constructively that every uniformly continuous convex function f:X→R + has positive infimum, where X is the convex hull of finitely many vectors. Using this result, we prove that a separating hyperplane theorem, the fundamental theorem of asset pricing, and Markov's principle are constructively equivalent. This is the first time that important theorems are classified into Markov's principle within constructive reverse mathematics.",
keywords = "Constructive mathematics, Markov's principle, Reverse mathematics, Separating hyperplane theorem, The fundamental theorem of asset pricing",
author = "Josef Berger and G. Svindland",
note = "Publisher Copyright: {\textcopyright} 2016 Elsevier B.V.",
year = "2016",
month = nov,
day = "1",
doi = "10.1016/j.apal.2016.05.003",
language = "English",
volume = "167",
pages = "1161--1170",
journal = "Annals of pure and applied logic",
issn = "0003-4843",
publisher = "Elsevier",
number = "11",

}

Download

TY - JOUR

T1 - A separating hyperplane theorem, the fundamental theorem of asset pricing, and Markov's principle

AU - Berger, Josef

AU - Svindland, G.

N1 - Publisher Copyright: © 2016 Elsevier B.V.

PY - 2016/11/1

Y1 - 2016/11/1

N2 - We prove constructively that every uniformly continuous convex function f:X→R + has positive infimum, where X is the convex hull of finitely many vectors. Using this result, we prove that a separating hyperplane theorem, the fundamental theorem of asset pricing, and Markov's principle are constructively equivalent. This is the first time that important theorems are classified into Markov's principle within constructive reverse mathematics.

AB - We prove constructively that every uniformly continuous convex function f:X→R + has positive infimum, where X is the convex hull of finitely many vectors. Using this result, we prove that a separating hyperplane theorem, the fundamental theorem of asset pricing, and Markov's principle are constructively equivalent. This is the first time that important theorems are classified into Markov's principle within constructive reverse mathematics.

KW - Constructive mathematics

KW - Markov's principle

KW - Reverse mathematics

KW - Separating hyperplane theorem

KW - The fundamental theorem of asset pricing

UR - http://www.scopus.com/inward/record.url?scp=84969960194&partnerID=8YFLogxK

U2 - 10.1016/j.apal.2016.05.003

DO - 10.1016/j.apal.2016.05.003

M3 - Article

VL - 167

SP - 1161

EP - 1170

JO - Annals of pure and applied logic

JF - Annals of pure and applied logic

SN - 0003-4843

IS - 11

ER -