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
2 - Stochastic Integrals and Differentials
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 necessary stochastic integral theory for processes of bounded variation is developed. The concept of predictability is discussed in detail, its interpretation as well as its relation to martingale theory. The Itô formula is derived and we prove the Watanabe characterization of the Poisson process.
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- Point Processes and Jump DiffusionsAn Introduction with Finance Applications, pp. 8 - 29Publisher: Cambridge University PressPrint publication year: 2021