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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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