Contents

pp v-x

Preface

pp xi-xii

Part I - Point Processes

pp 1-2

1 - Counting Processes

pp 3-7

2 - Stochastic Integrals and Differentials

pp 8-29

3 - More on Poisson Processes

pp 30-35

4 - Counting Processes with Stochastic Intensities

pp 36-42

5 - Martingale Representations and Girsanov Transformations

pp 43-55

6 - Connections between Stochastic Differential Equations and Partial Integro-Differential Equations

pp 56-63

7 - Marked Point Processes

pp 64-71

8 - The Itô Formula

pp 72-81

9 - Martingale Representation, Girsanov and Kolmogorov

pp 82-86

Part II - Optimal Control in Discrete Time

pp 87-88

10 - Dynamic Programming for Markov Processes

pp 89-98

Part III - Optimal Control in Continuous Time

pp 99-100

11 - Continuous-Time Dynamic Programming

pp 101-124

Part IV - Non-Linear Filtering Theory

pp 125-126

12 - Non-Linear Filtering with Wiener Noise

pp 127-140

13 - The Conditional Density

pp 141-148

14 - Non-Linear Filtering with Counting-Process Observations

pp 149-162

15 - Filtering with k-Variate Counting-Process Observations

pp 163-170

Part V - Applications in Financial Economics

pp 171-172

16 - Basic Arbitrage Theory

pp 173-187

17 - Poisson-Driven Stock Prices

pp 188-197

18 - The Simplest Jump-Diffusion Model

pp 198-205

19 - A General Jump-Diffusion Model

pp 206-219

20 - The Merton Model

pp 220-226

21 - Determining a Unique Q

pp 227-239

22 - Good-Deal Bounds

pp 240-248