Book contents
- Frontmatter
- Contents
- Preface
- Part I Point Processes
- 1 Counting Processes
- 2 Stochastic Integrals and Differentials
- 3 More on Poisson Processes
- 4 Counting Processes with Stochastic Intensities
- 5 Martingale Representations and Girsanov Transformations
- 6 Connections between Stochastic Differential Equations and Partial Integro-Differential Equations
- 7 Marked Point Processes
- 8 The Itô Formula
- 9 Martingale Representation, Girsanov and Kolmogorov
- Part II Optimal Control in Discrete Time
- Part III Optimal Control in Continuous Time
- Part IV Non-Linear Filtering Theory
- Part V Applications in Financial Economics
- References
- Index of Symbols
- Subject Index
5 - Martingale Representations and Girsanov Transformations
from Part I - Point Processes
Published online by Cambridge University Press: 27 May 2021
Book contents
- Frontmatter
- Contents
- Preface
- Part I Point Processes
- 1 Counting Processes
- 2 Stochastic Integrals and Differentials
- 3 More on Poisson Processes
- 4 Counting Processes with Stochastic Intensities
- 5 Martingale Representations and Girsanov Transformations
- 6 Connections between Stochastic Differential Equations and Partial Integro-Differential Equations
- 7 Marked Point Processes
- 8 The Itô Formula
- 9 Martingale Representation, Girsanov and Kolmogorov
- Part II Optimal Control in Discrete Time
- Part III Optimal Control in Continuous Time
- Part IV Non-Linear Filtering Theory
- Part V Applications in Financial Economics
- References
- Index of Symbols
- Subject Index
Summary
In this chapter we present and prove the Girsanov theorem for counting process. We also discuss (without proof) the martingale representation theorem. We then apply the Girsanov theory to Cox processes and maximum-likelihood estimation.
Keywords
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- Point Processes and Jump DiffusionsAn Introduction with Finance Applications, pp. 43 - 55Publisher: Cambridge University PressPrint publication year: 2021