This textbook covers the uniform laws of financial practice and classical methods for evaluating amortization, annuities, capital markets, interest rates, liability, sinking funds and term structures. An overview of stochastic processes and the Itô calculus, the main tool of stochastic finance, is provided. It then goes on to discuss the following classical fields: the evaluation of equity options, the interest rate stochastic models and their application to the bond option, the basis of quantitative risk management, the prudential rules for banks in the framework of the Basel II rules: value at risk (VarR and TVaR) models and portfolio choices. Finally, coverage is given to areas that are becoming increasingly important in finance: Markov and semi-Markov risk and evaluation models.
To help students in banking, business, economics and engineering master the complexities of these subjects, a comprehensive set of axioms for approaching financial problems is included.
1. Introductive Elements to Financial Mathematics.
2. Theory of Financial Laws.
3. Uniform Regimes in Financial Practice.
4. Financial Operations and their Evaluation: Decisional Criteria.
5. Annuities-Certain and their Value at Fixed Rate.
6. Loan Amortization and Funding Methods.
7. Exchanges and Prices on the Financial Market.
8. Annuities, Amortizations and Funding in the Case of Term Structures.
9. Time and Variability Indicators, Classical Immunization.
10. Basic Probabilistic Tools for Finance.
11. Markov Chains.
12. Semi-Markov Processes.
13. Stochastic or Itô Calculus.
14. Option Theory.
15. Markov and Semi-Markov Option Models.
16. Interest Rate Stochastic Models – Application to the Bond Pricing Problem.
17. Portfolio Theory.
18. Value at Risk (VaR) Methods and Simulation.
19. Credit Risk or Default Risk.
20. Markov and Semi-Markov Reward Processes and Stochastic Annuities.
Jacques Janssen teaches at the EURIA (Euro-Institut d’Actuariat, Brest, France) and is director of Jacan Insurance and Finance Services, a society of consulting and formation. He is member of many scientific associations and chairman of the International ASMDA Committee.
Raimondo Manca is Professor of Mathematics for Economics at University of Rome “La Sapienza”, Italy.
Ernesto Volpe di Prignano is Professor of Financial Mathematics at University of Rome “La Sapienza”, Italy.