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