Stochastic Calculus and Financial Applications

by J. Michael Steele

Contents
1. Random Walk and First Step Analysis 1

2. First Martingale Steps 11

3. Brownian Motion 29

4. Martingales: The Next Steps 43

5. Richness of Paths 61

6. Ito Integration 79

7. Localization and Ito's Integral 95

8. Ito's Formula 111

9. Stochastic Differential Equations 137

10. Arbitrage and SDEs 153

11. The Diffusion Equation 169

12. Representation Theorems 191

13. Girsanov Theory 213

14. Arbitrage and Martingales 233

15. The Feynman-Kac Connection 263

Appendix I. Mathematical Tools 277
Appendix II. Comments and Credits 285
Bibliography 293
Index 297