Teaching code

4S008402

Academic staff

Cecilia Mancini, Guido Gazzani

Coordinator

Cecilia Mancini

Credits

9

Language

Italian

Scientific Disciplinary Sector (SSD)

SECS-S/06 - MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES

Period

1st semester dal Oct 1, 2025 al Jan 30, 2026.

Courses Single

Authorized

Lessons timetable Moodle Seminars 0

Learning objectives

The aim of the first smaller part of the course is to present some tools and topics of classical financial mathematics (compounding regimes, mortgages, bonds). The second larger part of the lecture provides an in-depth introduction to modern financial mathematics and stochastic methods in discrete time (stochastic processes and martingales in discrete time) that are useful in view of more advanced lectures on the topic. Students will have the opportunity to learn the terminology and the concepts that are useful for the understanding and use the techniques of classical and modern mathematical finance. The lecture provides important examples of applications of concepts from the lectures on probability.

Prerequisites and basic notions

Analysis, Linear Algebra, Probability.

Program

Part 1: Classical financial mathematics - Reference book: Finance Manual.
1) Financial Regimes: financial operations, simple interest, capitalization of interest, exponential regime.
2) Annuities and amortization: non-elementary investments and financing, annuities with constant installments, accumulation plans, amortization plans, common forms of amortization, variable rate amortization.
3) Return for simple operations, Internal Rate of Return for compound operations
4) Bonds: bonds without coupons, bonds with fixed coupon. Term structure of interest rates, forward rates, securities indexed to interest rates
Part 2: modern mathematical finance under uncertainty - Reference book: Bjork
5) Review of fundamentals of probability theory: probability spaces, expected value, variance, conditional expected value, equivalent probabilities, sigma algebras, Martingales.
6) Discrete one-period market models: foundations and the fundamental theorem of asset pricing, contingent claims, market completeness.
7) Arbitrage theory in discrete multiperiod models: foundations on multiperiod models, absence of arbitrage, pricing and hedging of European contingent claims

Bibliography

Didactic methods

Frontal lessons and exercises in class. The collaboration of a tutor is scheduled for further exercises. Attendance in class is highly recommended, to benefit from the fundamental interaction and exchange

Learning assessment procedures

Written exam of two hours. The exam will contain exercises and questions on theory (statements and demonstrations). The exam is passed if the written exam has achieved at least 18 out of 33 points. An oral exam may be requested by the teacher, and if so it will be mandatory, to clarify the evaluation of the written exam.
The following will be verified:
- knowledge and understanding of the fundamental concepts of classical financial mathematics
- knowledge and understanding of the fundamental concepts of modern stochastic mathematical finance
- the ability to analyze, synthesize, abstract and logical reasoning
- the ability to apply this knowledge to solve problems and exercises, in a reasoned way.

Evaluation criteria

Mathematical rigor in procedures and demonstrations. Acquired financial sensitivity. Correctness of calculations.

Criteria for the composition of the final grade

It will be decided in class at the beginning of the course whether to take a midterm test. In this case, if at least a grade of 16 out of 33 is achieved in the midterm test, this will count for 50% of the final grade. The second midterm test can only be taken at the first exam of the winter session.

Exam language

Italiano