Point Processes and Jump Diffusions
An Introduction with Finance Applications

Develop a deep understanding and working knowledge of point-process theory as well as its applications in finance.

Tomas Björk (Author)

9781316518670, Cambridge University Press

Hardback, published 17 June 2021

320 pages
25 x 17.4 x 2.1 cm, 0.68 kg

'essential for those who are interested in the theory of point processes, in both theoretical and applied aspects.' Ying Hui Dong, MathSciNet

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.

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: 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.

Subject Areas: Mathematical foundations [PBC], Insurance law [LNPN], Finance [KFF], Financial accounting [KFCF]