The teaching unit covers the fundamentals of classical financial mathematics and actuarial mathematics, with fccus on financial operations that is the exchange of monetary amounts due at different maturities.
The teaching unit contributes at providing the students with mathematical tools to formalize and model financial transactions, both certain and random, as well as the main life insurance operations.
At the end of the teaching unit, the student will be able to:
- Apply main financial laws (content) to transactions involving monetary amounts with different maturities (condition).
- Calculate the present and future value of discrete annuities and loans (content) under different financial regimes (condition).
- Analyze and evaluate amortization schedules and capital formation (content) in real-world contexts (condition).
- Evaluate bonds and calculate the effective yield (content) using market data (condition).
- Apply basic actuarial models (content) to simple life insurance contracts (condition).
Basic knowledge of mathematics is required, in particular algebra and calculus..
Lectures and classroom exercises.
Attendance is not compulsory.
Students with a disability, DSA or special educational needs certification must contact, at the beginning of the lessons, both the instructor and the Department's disability contact, Prof.ssa Elena Lagomarsino (elena.lagomarsino@unige.it), , to agree on teaching and exam methods that, in compliance with the teaching unit objectives, 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 under different regimes.. Nominal annual interest and discount rates convertible k times per year. Corresponding rates. Average rate.
Part II: Discrete annuities and their valuation. Notes on 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. Notes on amortization and capital formation under continuous capitalization. Valuation 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. Valuation 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. Some life insurance operations.. Premia..
Specific information on the reference bibliography will be provided by the instructor at the beginning of the lessons.
Ricevimento: Office hours will be communicated at the beginning of the lessons. Students can contact the instructor by email at marina.resta@unige.it.
I semester: fron Monday, 15 September 2025 to Friday, 12 December 2025.
The exam is oral and includes both theoretical questions and practical exercises. No minimum thresholds or separate parts are foreseen. Alternative arrangements for Erasmus students will be eventually agreed with the instructor.
The assessment of learning outcomes is carried out through an oral exam, consisting of theoretical questions and/or practical exercises covering all topics of the syllabus. The evaluation considers clarity of exposition, correct use of terminology, ability to apply acquired knowledge, and problem-solving skills.
Students must book the exam on the dedicated portal. The exam can be taken two times out of three in each session (summer and winter). For further information not included in the teaching unit description, please contact the instructor.
