Point Processes and Jump Diffusions
An Introduction with Finance Applications
Published on 17. June 2021
Book
Hardback
320 pages
978-1-316-51867-0 (ISBN)
Description
The theory of marked point processes on the real line is of great and increasing importance in areas such as insurance mathematics, queuing theory and financial economics. However, the theory is often viewed as technically and conceptually difficult and has proved to be a block for PhD students looking to enter the area. This book gives an intuitive picture of the central concepts as well as the deeper results, while presenting the mathematical theory in a rigorous fashion and discussing applications in filtering theory and financial economics. Consequently, readers will get a deep understanding of the theory and how to use it. A number of exercises of differing levels of difficulty are included, providing opportunities to put new ideas into practice. Graduate students in mathematics, finance and economics will gain a good working knowledge of point-process theory, allowing them to progress to independent research.
Reviews / Votes
'essential for those who are interested in the theory of point processes, in both theoretical and applied aspects.' Ying Hui Dong, MathSciNetMore details
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises
Dimensions
Height: 250 mm
Width: 175 mm
Thickness: 22 mm
Weight
737 gr
ISBN-13
978-1-316-51867-0 (9781316518670)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
E-Book
06/2021
Cambridge University Press
€47.49
Available for download
Person
Tomas Bjoerk is Professor Emeritus of Mathematical Finance at the Stockholm School of Economics and previously worked at the Mathematics Department of the Royal Institute of Technology, Stockholm. Bjoerk has been co-editor of Mathematical Finance, on the editorial board for Finance and Stochastics and several other journals, and was President of the Bachelier Finance Society. He is particularly known for his research on point-process-driven forward-rate models, finite-dimensional realizations of infinite dimensional SDEs, and time-inconsistent control theory. He is the author of the well-known textbook Arbitrage Theory in Continuous Time (1998), now in its fourth edition.
Content
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 Ito formula; 9. Martingale representation, Girsanov and Kolmogorov; Part II. Optimal Control in Discrete Time: 10. Dynamic programming for Markov processes; Part III. Optimal Control in Continuous Time: 11. Continuous-time dynamic programming; Part IV. Non-Linear Filtering Theory: 12. Non-linear filtering with Wiener noise; 13. The conditional density; 14. Non-linear filtering with counting-process observations; 15. Filtering with k-variate counting-process observations; Part VI. Applications in Financial Economics: 16. Basic arbitrage theory; 17. Poisson-driven stock prices; 18. The simplest jump-diffusion model; 19. A general jump-diffusion model; 20. The Merton model; 21. Determining a unique Q; 22. Good-deal bounds; 23. Diversifiable risk; 24. Credit risk and Cox processes; 25. Interest-rate theory; 26. Equilibrium theory; References; Index of symbols; Subject index.