Teaching code

4S008402

Teacher

Cecilia Mancini

Coordinator

Cecilia Mancini

Credits

9

Language

Italian

Scientific Disciplinary Sector (SSD)

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

Period

Semester 1  dal Oct 1, 2024 al Jan 31, 2025.

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 text: 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 conditions of uncertainty - Reference texts: Bjork
5) Review of fundamentals of probability theory: probability spaces, expected value, variance, conditional expected value, equivalent probabilities, sigma algebras, Martingale.
6) Discrete uniperiod 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, contingentclaimseurope
Preferences and risk aversion.
Time permitting: expected utility criterion. Mean-variance criterion and static portfolio optimization. CAPM

Bibliography

Didactic methods

Frontal lesson.

Learning assessment procedures

Written exam of two hours. The tests will contain exercises and questions on theory (proof of statements). The exam is passed if the written test has achieved at least a score of 18 out of 33. An oral exam may be requested by the teacher, and if so it will be mandatory, to clarify the evaluation of the written test. 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

If in the intermediate test at least a grade of 16 out of 33 is achieved, this contributes 50% to the final grade.

Exam language

italiana