Mathematical Finance: Deterministic and Stochastic Models

Preface  xvii

Part I. Deterministic Models 1

Chapter 1. Introductory Elements to Financial Mathematics 3

Chapter 2. Theory of Financial Laws 13

Chapter 3. Uniform Regimes in Financial Practice 41

Chapter 4. Financial Operations and their Evaluation: Decisional Criteria 91

Chapter 5. Annuities-Certain and their Value at Fixed Rate 147

Chapter 6. Loan Amortization and Funding Methods 211

Chapter 7. Exchanges and Prices on the Financial Market 289

Chapter 8. Annuities, Amortizations and Funding in the Case of Term Structures 331

Chapter 9. Time and Variability Indicators, Classical Immunization 363

Part II. Stochastic Models 409

Chapter 10. Basic Probabilistic Tools for Finance 411

Chapter 11. Markov Chains 457

Chapter 12. Semi-Markov Processes  481

Chapter 13. Stochastic or Itô Calculus 517

Chapter 14. Option Theory 553

Chapter 15. Markov and Semi-Markov Option Models 607

Chapter 16. Interest Rate Stochastic Models – Application to the Bond Pricing Problem 641

Chapter 17. Portfolio Theory 687

Chapter 18. Value at Risk (VaR) Methods and Simulation 703

Chapter 19. Credit Risk or Default Risk 743

Chapter 20. Markov and Semi-Markov Reward Processes and Stochastic Annuities 791

References 831

Index 839