Mathematical Finance: Deterministic Models and Stochastic Models

This book provides a detailed study of Financial Mathematics. In addition to the extraordinary depth the book provides, it offers a study of the axiomatic approach that is ideally suited for analyzing financial problems. This book is addressed to MBA's, Financial Engineers, Applied Mathematicians, Banks, Insurance Companies, and Students of Business School, of Economics, of Applied Mathematics, of Financial Engineering, Banks, and more.

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 Ito 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