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Arbitrage Theory in Continuous Time

Tomas Björk

Published in print:
2004
Published Online:
October 2005
ISBN:
9780199271269
eISBN:
9780191602849
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/0199271267.001.0001
Subject:
Economics and Finance, Financial Economics

This book presents an introduction to arbitrage theory and its applications to problems for financial derivatives. This second edition includes more advanced materials; appendices on measure theory, ... More


Black–Scholes from a Martingale Point of View*

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:
10.1093/0199271267.003.0012
Subject:
Economics and Finance, Financial Economics

This chapter discusses the standard Black-Scholes model from the martingale point of view. The probability space (Ω, □, P, □-) carrying a P-Wiener process W-, where the filtration □- is the one ... More


 Taking Chances

Ken Binmore

in Playing for Real: Game Theory

Published in print:
2007
Published Online:
May 2007
ISBN:
9780195300574
eISBN:
9780199783748
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195300574.003.0003
Subject:
Economics and Finance, Microeconomics

This chapter shows how risk can be introduced into the rules of a game by admitting chance moves. The Monty Hall problem is offered as an example. Elementary probability theory is reviewed, and ... More


Are there discontinuities in financial prices?

Neil Shephard

in Celebrating Statistics: Papers in honour of Sir David Cox on his 80th birthday

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198566540
eISBN:
9780191718038
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566540.003.0012
Subject:
Mathematics, Probability / Statistics

This chapter explores whether there are discontinuities in financial price processes using daily data on the Japanese yen and United States dollar. It opens with a brief description of the data, ... More


PROBABILISTIC INGREDIENTS

Mathew Penrose

in Random Geometric Graphs

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198506263
eISBN:
9780191707858
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198506263.003.0002
Subject:
Mathematics, Probability / Statistics

This chapter derives some probabilistic results for later use. A dependency graph for a family of random variables is a deterministic graph with vertex-set identified with the random variables and ... More


Estimating functions

Christopher G. Small and Jinfang Wang

in Numerical Methods for Nonlinear Estimating Equations

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198506881
eISBN:
9780191709258
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198506881.003.0002
Subject:
Mathematics, Probability / Statistics

This chapter gives a survey of the basic concepts of estimating functions, which are used in subsequent chapters. The concept of unbiasedness for estimating functions is introduced as a ... More


Stochastic Analysis and Diffusion Processes

Gopinath Kallianpur and P Sundar

Published in print:
2014
Published Online:
April 2014
ISBN:
9780199657063
eISBN:
9780191781759
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199657063.001.0001
Subject:
Mathematics, Probability / Statistics, Applied Mathematics

Starting with the construction of stochastic processes, the book introduces Brownian motion and martingales. After proving the Doob-Meyer decomposition, quadratic variation processes and local ... 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


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


Linear Stochastic Difference Equations

Lars Peter Hansen and Thomas J. Sargent

in Recursive Models of Dynamic Linear Economies

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691042770
eISBN:
9781400848188
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691042770.003.0002
Subject:
Economics and Finance, History of Economic Thought

This chapter describes the vector first-order linear stochastic difference equation. It is first used to represent information flowing to economic agents, then again to represent competitive ... More


Theoretical Foundations

Angus Deaton

in Understanding Consumption

Published in print:
1992
Published Online:
November 2003
ISBN:
9780198288244
eISBN:
9780191596131
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198288247.003.0001
Subject:
Economics and Finance, Macro- and Monetary Economics

Reviews the basic micro‐foundations of intertemporal choice under uncertainty, and considers the implications for the macroeconomic aggregates of consumption and savings. It also reviews the ... 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


Martingales

James Davidson

in Stochastic Limit Theory: An Introduction for Econometricians

Published in print:
1994
Published Online:
November 2003
ISBN:
9780198774037
eISBN:
9780191596117
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198774036.003.0015
Subject:
Economics and Finance, Econometrics

This chapter summarizes the essentials of sequential conditioning and martingale theory. After a review of the basic properties of martingales and semi‐martingales, the upcrossing inequality and ... More


Convergence in Lp Norm

James Davidson

in Stochastic Limit Theory: An Introduction for Econometricians

Published in print:
1994
Published Online:
November 2003
ISBN:
9780198774037
eISBN:
9780191596117
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198774036.003.0019
Subject:
Economics and Finance, Econometrics

This chapter looks in detail at proofs of the weak law of large numbers (convergence in probability) using the technique of establishing convergence in LP‐norm. The extension to a proof of ... More


The Strong Law of Large Numbers

James Davidson

in Stochastic Limit Theory: An Introduction for Econometricians

Published in print:
1994
Published Online:
November 2003
ISBN:
9780198774037
eISBN:
9780191596117
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198774036.003.0020
Subject:
Economics and Finance, Econometrics

This chapter focuses largely on methods of proof of the strong law, building on the fundamental convergence lemma. It covers Kolmogorov's three‐series theorem, strong laws for martingales, random ... More


CLTs for Dependent Processes

James Davidson

in Stochastic Limit Theory: An Introduction for Econometricians

Published in print:
1994
Published Online:
November 2003
ISBN:
9780198774037
eISBN:
9780191596117
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198774036.003.0024
Subject:
Economics and Finance, Econometrics

This chapter deals with the central limit theorem (CLT) for dependent processes. As with the law of large numbers, the focus is on near‐epoch dependent and mixing processes, and array versions of the ... More


Weak Convergence to Stochastic Integrals

James Davidson

in Stochastic Limit Theory: An Introduction for Econometricians

Published in print:
1994
Published Online:
November 2003
ISBN:
9780198774037
eISBN:
9780191596117
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198774036.003.0030
Subject:
Economics and Finance, Econometrics

The main object of this final chapter is to prove an essential companion result to the FCLT, the convergence of certain normalized random sums to stochastic integrals with respect to Brownian motion. ... More


The Martingale Approach to Arbitrage Theory

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:
10.1093/0199271267.003.0010
Subject:
Economics and Finance, Financial Economics

This chapter analyses a market model made up of N + 1 a priori given asset price processes S0, S1, ..., SN. Typically, the model is specified by giving the dynamics of the asset price processes under ... More


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


Incomplete Markets

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:
10.1093/0199271267.003.0015
Subject:
Economics and Finance, Financial Economics

This chapter examines derivative pricing in incomplete markets. It focuses on a particular type of incomplete market, namely a “factor model” — a market where there are some nontraded underlying ... More


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