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
