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Multidimensional Models: Martingale Approach

Tomas Björk

in Arbitrage Theory in Continuous Time

Published in print:
2004
Published Online:
October 2005
ISBN:
9780199271269
eISBN:
9780191602849
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199271267.003.0014
Subject:
Economics and Finance, Financial Economics

This chapter analyses a multidimensional model using the martingale machinery of Chapter 10. This model is more general than the one used in the previous chapter to obtain more general results, and ... More


The Process and Its Profiles

John Hicks

in Capital and Time: A Neo-Austrian Theory

Published in print:
1987
Published Online:
November 2003
ISBN:
9780198772866
eISBN:
9780191596414
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198772866.003.0002
Subject:
Economics and Finance, Macro- and Monetary Economics

This chapter begins with a discussion of the productive process, which is defined as a scheme by which a flow of inputs is converted into a flow of outputs. It then examines the viability of ... More


Selection

Graham K. Taylor and Adrian L. R. Thomas

in Evolutionary Biomechanics

Published in print:
2014
Published Online:
April 2014
ISBN:
9780198566373
eISBN:
9780191779459
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566373.003.0002
Subject:
Biology, Evolutionary Biology / Genetics, Ornithology

This chapter develops a model of adaptive evolution that is founded upon the genetical theory of natural selection, and which justifies the adaptationist approach of analysing traits at organismal ... More


The Martingale Approach to Arbitrage Theory

Tomas Björk

in Arbitrage Theory in Continuous Time

Published in print:
2019
Published Online:
February 2020
ISBN:
9780198851615
eISBN:
9780191886218
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198851615.003.0011
Subject:
Economics and Finance, Econometrics

In this chapter the theoretical level is substantially increased, and we discuss in detail the deep connection between financial pricing theory and martingale theory. The first main result of the ... More


Euclid's Elements 9. 14 and the Fundamental Theorem of Arithmetic

C. M. Taisbak

in Science and Mathematics in Ancient Greek Culture

Published in print:
2002
Published Online:
February 2010
ISBN:
9780198152484
eISBN:
9780191710049
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198152484.003.0013
Subject:
Classical Studies, European History: BCE to 500CE

This chapter clarifies some unfamiliar concepts of Euclidean number theory and examines the bricks, constituents, and formative elements of numbers. It also considers three famous propositions from ... More


ARBITRAGE-FREE PRICING IN COMPLETE MARKETS

Patrick L. Anderson

in The Economics of Business Valuation: Towards a Value Functional Approach

Published in print:
2013
Published Online:
September 2013
ISBN:
9780804758307
eISBN:
9780804783224
Item type:
chapter
Publisher:
Stanford University Press
DOI:
10.11126/stanford/9780804758307.003.0010
Subject:
Economics and Finance, Financial Economics

The author describes one of the breakthrough concepts of modern finance: the use of the no arbitrage principle in complete markets as the basis for the powerful mathematics of “risk neutral” or ... More


A More General One Period Model

Tomas Björk

in Arbitrage Theory in Continuous Time

Published in print:
2019
Published Online:
February 2020
ISBN:
9780198851615
eISBN:
9780191886218
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198851615.003.0003
Subject:
Economics and Finance, Econometrics

In this chapter we study a general one period model living on a finite sample space. The concepts of no arbitrage and completeness are introduced, as well as the concept of a martingale measure. We ... More


Fixed Point Buildings

Bernhard M¨uhlherr, Holger P. Petersson, and Richard M. Weiss

in Descent in Buildings (AM-190)

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691166902
eISBN:
9781400874019
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691166902.003.0022
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter presents the proof for the Fundamental Theorem of Descent in buildings: that if Γ‎ is a descent group, the set of residues of a building Δ‎ that are stabilized by a subgroup Γ‎ of ... More


Prime numbers: The DNA of mathematics

Marcel Danesi

in Pythagoras' Legacy: Mathematics in Ten Great Ideas

Published in print:
2020
Published Online:
January 2020
ISBN:
9780198852247
eISBN:
9780191886959
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198852247.003.0002
Subject:
Mathematics, History of Mathematics, Educational Mathematics

The Pythagoreans developed many of the ideas related to numbers that have become so familiar to us, including even and odd numbers, square numbers, triangular numbers, and so on. They also discovered ... More


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