Combining intuitive understanding with rigorous mathematical theory, this book introduces the theory of marked point processes on the real line, including filtering and application to financial economics. Graduate-level mathematicians and economists will gain a working knowledge of the field and a deep understanding of the key concepts and proofs.
Combining intuitive understanding with rigorous mathematical theory, this book introduces the theory of marked point processes on the real line, including filtering and application to financial economics. Graduate-level mathematicians and economists will gain a working knowledge of the field and a deep understanding of the key concepts and proofs.
Tomas Björk 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. Björk 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.
Inhaltsangabe
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.
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.
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