The teaching unit offers topics in classical financial mathematics and actuarial mathematics.
The aim of the course is to provide formalization and mathematical modeling of financial transactions. In addition, with reference to random financial transactions, the course provides mathematical models and methods for some life-insurance contracts.
At the end of the teaching unit, the student will be able to:
- Apply the main techniques of classical financial mathematics to the evaluation of financial transactions under standard conditions;
- Analyze and solve problems related to life insurance contracts using basic actuarial models;
- Calculate present and future values of financial flows in different capitalization regimes, given the required parameters
Basic knowledge of general mathematics is required.
The teaching unit includes lectures with theoretical parts and written exercises. Attendance is not compulsory. Students with certification of disability, specific learning disorders (DSA), or special educational needs should contact both the instructor and the Department’s disability liaison, Prof.ssa Elena Lagomarsino (elena.lagomarsino@unige.it), , at the beginning of the course to agree on teaching and examination arrangements that, while respecting the objectives of the teaching unit, take into account individual learning methods and allow the use of any compensatory tools
Part I: Theory of financial laws. Uniform financial laws over time, laws additive with respect to capital, decomposable and separable laws. Main financial regimes. Simple interest. Compound capitalization, mixed and exponential conventions. Continuous capitalization. Commercial discount, rational discount, and compound discount. Present and discounted values. Capitalization and discount factors. Separability. Equivalent interest and discount rates. Nominal annual interest and discount rates convertible k times per year. Corresponding rates. Average rate. Part II: Discrete certain annuities and their evaluation. Introduction to continuous annuities and their evaluation. Part III: Amortization of a single loan and capital formation. Amortization and capital formation under compound capitalization. Amortization payments, principal and interest components. Extinguished and outstanding debt. Various amortization methods. Introduction to amortization and capital formation under continuous capitalization. Evaluation of single loans. Value, bare ownership, and usufruct. Part IV: Loans divided into securities. Securities with full capitalization. Securities with coupons redeemable at a certain maturity. Effective interest rate of the entire loan. Evaluation of divided loans. Price and yield of securities redeemable at a certain maturity. Volatility of a security. Part V: Term structure of interest rates. Part VI: Random financial transactions. Introduction to the choice among random financial transactions. Some life insurance operations. Premiums.
Specific information on the reference bibliography will be provided by the instructor at the beginning of the lessons and published on Aulaweb
Ricevimento: MARINA RAVERA: Student reception (remotely via Teams or in person) must be arranged with the instructor by email appointment
Lessons will start in the first semester. For the exact date, please refer to the lesson calendar published on the Department website.
The exam will be oral
The exam will be oral with questions aimed at evaluating knowledge and skills, in particular: - the ability to apply financial mathematics techniques to specific problems; - clarity of exposition and correct use of terminology; - the ability to analyze and solve basic actuarial problems
Please contact the instructor for further information not included in the teaching unit description.
