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Randomness and betting strategies

André Nies

in Computability and Randomness

Published in print:
2009
Published Online:
May 2009
ISBN:
9780199230761
eISBN:
9780191710988
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199230761.003.0007
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

Martingales form the mathematical counterpart of betting strategies. This chapter studies computable randomness, where the tests are computable martingales, and separates it from both Martin–Löf ... More


Optimal Fiscal Policy in a Linear Stochastic Economy

Thomas J. Sargent and François R. Velde

in Computational Methods for the Study of Dynamic Economies

Published in print:
2001
Published Online:
November 2003
ISBN:
9780199248278
eISBN:
9780191596605
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199248273.003.0009
Subject:
Economics and Finance, Macro- and Monetary Economics

The Lucas and Stokey (1983) economy without capital is used to exhibit features of the Lucas and Stokey model of optimal taxation, and show how they compare with Barro's (1979) tax‐smoothing model. ... More


The Mathematics of the 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:
10.1093/0199271267.003.0011
Subject:
Economics and Finance, Financial Economics

This chapter presents the two main workhorses of the martingale approach to arbitrage theory: the Martingale Representation Theorem and the Girsanov Theorem. The Martingale Representation Theorem ... More


The Structure of Radical Probabilism

Brian Skyrms

in From Zeno to Arbitrage: Essays on Quantity, Coherence, and Induction

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199652808
eISBN:
9780191745829
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199652808.003.0011
Subject:
Philosophy, Philosophy of Science, Metaphysics/Epistemology

Does radical probabilism have enough structure to say anything interesting? Structure is provided by coherent belief change. Coherence imposes the Martingale property, which gives convergence ... More


Introduction

Stéphane Boucheron, Gábor Lugosi, and Pascal Massart

in Concentration Inequalities: A Nonasymptotic Theory of Independence

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199535255
eISBN:
9780191747106
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199535255.003.0001
Subject:
Mathematics, Probability / Statistics, Applied Mathematics

In this introductory chapter we briefly review the history of the subject and outline the contents, as an appetizer for the rest of the book.


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