Details
| Original language | English |
|---|---|
| Title of host publication | Proof and Computation |
| Subtitle of host publication | Digitization in Mathematics, Computer Science and Philosophy |
| Pages | 53-82 |
| Number of pages | 30 |
| ISBN (electronic) | 9789813270947 |
| Publication status | Published - 2018 |
| Externally published | Yes |
Abstract
Working within Bishop-style constructive mathematics, we show that positive-valued, uniformly continuous, convex functions defined on convex and compact subsets of Rn have positive infimum. This gives rise to a separation theorem for convex sets. Based on these results, we show that the fundamental theorem of asset pricing is constructively equivalent to Markov’s principle. The philosophical background behind all this is a constructively valid convex version of Brouwer’s fan theorem. The emerging comprehensive yet concise overall picture of assets, infima of functions, separation of convex sets, and the fan theorem indicates that mathematics in convex environments has some innate constructive nature.
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
- Computer Science(all)
- General Computer Science
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Proof and Computation: Digitization in Mathematics, Computer Science and Philosophy. 2018. p. 53-82.
Research output: Chapter in book/report/conference proceeding › Contribution to book/anthology › Research › peer review
}
TY - CHAP
T1 - Constructive convex programming
AU - Berger, Josef
AU - Svindland, G.
N1 - Publisher Copyright: © 2018 by World Scientific Publishing Co. Pte. Ltd.
PY - 2018
Y1 - 2018
N2 - Working within Bishop-style constructive mathematics, we show that positive-valued, uniformly continuous, convex functions defined on convex and compact subsets of Rn have positive infimum. This gives rise to a separation theorem for convex sets. Based on these results, we show that the fundamental theorem of asset pricing is constructively equivalent to Markov’s principle. The philosophical background behind all this is a constructively valid convex version of Brouwer’s fan theorem. The emerging comprehensive yet concise overall picture of assets, infima of functions, separation of convex sets, and the fan theorem indicates that mathematics in convex environments has some innate constructive nature.
AB - Working within Bishop-style constructive mathematics, we show that positive-valued, uniformly continuous, convex functions defined on convex and compact subsets of Rn have positive infimum. This gives rise to a separation theorem for convex sets. Based on these results, we show that the fundamental theorem of asset pricing is constructively equivalent to Markov’s principle. The philosophical background behind all this is a constructively valid convex version of Brouwer’s fan theorem. The emerging comprehensive yet concise overall picture of assets, infima of functions, separation of convex sets, and the fan theorem indicates that mathematics in convex environments has some innate constructive nature.
UR - http://www.scopus.com/inward/record.url?scp=85051620242&partnerID=8YFLogxK
U2 - 10.1142/9789813270947_0002
DO - 10.1142/9789813270947_0002
M3 - Contribution to book/anthology
SN - 9789813270930
SP - 53
EP - 82
BT - Proof and Computation
ER -