Point Processes and Jump Diffusions

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.