Mathematical Finance

Jacques Janssen is Honorary Professor at the Solvay Business School in Brussels, Belgium. He has previously taught at EURIA and been a director of Jacan Insurance and Finance Services, a consultancy and training company.Raimondo Manca is professor of mathematical methods applied to economics, finance and actuarial science at University of Rome "La Sapienza" in Italy. He is associate editor for the journal Methodology and Computing in Applied Probability. His main research interests are multidimensional linear algebra, computational probability, application of stochastic processes to economics, finance and insurance and simulation models.

• Preface  xviiPart I. Deterministic Models 1Chapter 1. Introductory Elements to Financial Mathematics 3Chapter 2. Theory of Financial Laws 13Chapter 3. Uniform Regimes in Financial Practice 41Chapter 4. Financial Operations and their Evaluation: Decisional Criteria 91Chapter 5. Annuities-Certain and their Value at Fixed Rate 147Chapter 6. Loan Amortization and Funding Methods 211Chapter 7. Exchanges and Prices on the Financial Market 289Chapter 8. Annuities, Amortizations and Funding in the Case of Term Structures 331Chapter 9. Time and Variability Indicators, Classical Immunization 363Part II. Stochastic Models 409Chapter 10. Basic Probabilistic Tools for Finance 411Chapter 11. Markov Chains 457Chapter 12. Semi-Markov Processes  481Chapter 13. Stochastic or Itô Calculus 517Chapter 14. Option Theory 553Chapter 15. Markov and Semi-Markov Option Models 607Chapter 16. Interest Rate Stochastic Models – Application to the Bond Pricing Problem 641Chapter 17. Portfolio Theory 687Chapter 18. Value at Risk (VaR) Methods and Simulation 703Chapter 19. Credit Risk or Default Risk 743Chapter 20. Markov and Semi-Markov Reward Processes and Stochastic Annuities 791References 831Index 839