Point processes and jump diffusions : an introduction with finance applications
著者
書誌事項
Point processes and jump diffusions : an introduction with finance applications
Cambridge University Press, 2021
- : hbk
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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.
目次
- 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.
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