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
7 - Marked Point Processes
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
The theory is here generalized to include marked point processes (MPP) on the real line with ageneral mark space. We define and interpret MPP differentials and integrals The compensator and intensity of an MPP is discussed carefully. We present the relevant predictability concept for MPP integrands, andthe connection between MPP integrals and martingales is discussed in detail.
Keywords
- Type
- Chapter
- Information
- Point Processes and Jump DiffusionsAn Introduction with Finance Applications, pp. 64 - 71Publisher: Cambridge University PressPrint publication year: 2021