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
8 - The Itô Formula
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
We derive the relevant Itô formula for jump diffusions driven by a marked point process. The compound Poisson process is introduced, and we also study the MPP versions of the linear and geometric SDE.
Keywords
- Type
- Chapter
- Information
- Point Processes and Jump DiffusionsAn Introduction with Finance Applications, pp. 72 - 81Publisher: Cambridge University PressPrint publication year: 2021