## 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 L_{p} 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