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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


Existence and the Mathematics of Selection: The Adaptive Landscape versus the Fundamental Theorem

John O. Reiss

in Not by Design: Retiring Darwin's Watchmaker

Published in print:
2009
Published Online:
March 2012
ISBN:
9780520258938
eISBN:
9780520944404
Item type:
chapter
Publisher:
University of California Press
DOI:
10.1525/california/9780520258938.003.0007
Subject:
Biology, Evolutionary Biology / Genetics

Darwin's separation between adaptedness and existence entered into modern evolutionary theory at its root, in the population genetics work of Sewall Wright and J. B. S. Haldane. This chapter shows ... More


Theorems of Natural Selection: Results of Price, Fisher, and Robertson

Bruce Walsh and Michael Lynch

in Evolution and Selection of Quantitative Traits

Published in print:
2018
Published Online:
September 2018
ISBN:
9780198830870
eISBN:
9780191868986
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198830870.003.0006
Subject:
Biology, Evolutionary Biology / Genetics, Biochemistry / Molecular Biology

This chapter reviews a number of “theorems” of natural selection. These include exact results (true mathematical theorems): the Robertson-Price identity, Price's general expression for any form of ... 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


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


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


Wright’s Adaptive Landscape, Fisher’s Fundamental Theorem

Samir Okasha

in Agents and Goals in Evolution

Published in print:
2018
Published Online:
July 2018
ISBN:
9780198815082
eISBN:
9780191852909
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198815082.003.0004
Subject:
Philosophy, Philosophy of Science, Philosophy of Mind

Fitness maximization, or optimization, is a controversial idea in evolutionary biology. One classical formulation of this idea is that natural selection will tend to push a population up a peak in an ... 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


i: Imaginary numbers

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/9780198852247.003.0007
Subject:
Mathematics, History of Mathematics, Educational Mathematics

What kind of number is √−1? In a way that parallels the unexpected discovery of √2 by the Pythagoreans, when this number surfaced as a solution to a quadratic equation, mathematicians asked ... 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


Associative Effects: Competition, Social Interactions, Group and Kin Selection

Bruce Walsh and Michael Lynch

in Evolution and Selection of Quantitative Traits

Published in print:
2018
Published Online:
September 2018
ISBN:
9780198830870
eISBN:
9780191868986
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198830870.003.0022
Subject:
Biology, Evolutionary Biology / Genetics, Biochemistry / Molecular Biology

The phenotypes of those individuals with which an focal individual interacts often influences the trait value in the focal individual. Maternal effects is a classic example of this phenomena, as is ... More


Business Ethics and Efficiency: The Market Failures Approach

Abraham A. Singer

in The Form of the Firm: A Normative Political Theory of the Corporation

Published in print:
2018
Published Online:
November 2018
ISBN:
9780190698348
eISBN:
9780190909499
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780190698348.003.0012
Subject:
Political Science, Political Theory

This and the next chapter articulate a theory of business ethics that fits with how the book has approached corporate governance and corporate law. It takes the “market failures approach” (MFA) to ... More


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