Academic Year 2021-2022

FINANCIAL MATHEMATICS

Teachers

Antonino Zanette
Unit Credits
6
Teaching Period
First Period
Course Type
Supplementary
Prerequisites. The course takes place in the first semester of the second Bachelor degree year.

Mathematics (general) is the bridging course.

Prerequisites are knowledge of elementary functions and their graphical representation, ability in (elementary) limits calculation, knowledge of some notable special limits, knowledge of basic differential and integral calculus.

Teaching Methods. Slides cover the whole program. They are only a part of material, consisting in one recommended text on mathematics for finance and notes by the teacher on probability. Both slides and notes can be found in the Educational material of the course. The teacher suggests additional material that can be found in Internet and reference books for further insights.

There will be theoretical lessons with examples and applications and practice exercises taken from previous exams. Exam texts with solution are also available in the Educational material.

Verification of Learning. The exam consists in: • Two and a half-hours written examination at the end of the course (compulsory); • oral examination ONLY for students with score less than 18 or greater than 25. The oral examination can modify the written test score from -3 to +3. Students with an insufficient score must do the oral examination in order to reaching final sufficiency (if they really want to improve, they can repeat the written exam). Students with score greater than 25 must do the oral examination and must have knowledge and mastery on the whole program.

In the written test there are both numerical exercises and theoretical questions.

More Information. There are no contents/program differences between attending and not attending students. To the last students we suggest to look at the “Educational material” (e-learning platform) and to attend to the tutorial hours (see the timetable on the University web-site) for explanations.

Topics encountered during the course are suitable to Business and Economics bachelor thesis. Thesis will be quantitative and require the adoption of adequate mathematical tools.

Objectives
Skills

The first part of the course provides the fundamentals of financial mathematics under certainty conditions. The second part is devoted to elements of probability theory, revisited from a financial point of view. This will allow students to consider financial mathematics applications in stochastic frameworks (i.e. applications in portfolio theory and in actuarial fields). At the end of the course students will be able to:

• knowing and managing interest, discount, final value, present value, rates, capitalization and discount factors;

• using different accumulation and discount functions;

• linking the properties of financial functions with arbitrage free assumptions under certainty conditions;

• making financial evalutations under no flat yield curves;

• evaluating annuities;

• writing amortization schedules;

• evaluating enterpreneurial projects;

• giving a financial meaning to probabilities and proving the fundamental probability theorems with the no arbitrage assumption;

• knowing the ways to characterize (discrete and continuous) random variables probability distributions;

• knowing the most important synthetic distribution indices and giving them a financial meaning when the random variables are stochastic assets returns;

• applying the financial and probabilistic tools to decisions under uncertainty (in particular to portfolio choices and to evaluation of life insurance premiums).

Soft skills:

• the student should reach a financial literacy level so that he will be able to identifying and analyzing financial information, solving financial problems;

• students should become aware of the importance of risk in financial investing, in financial planning and in stochastic asset pricing;

• topics handled during the course are fundamental for advanced course in quantitative finance;

• both under certainty and uncertainty we give relevance to the no arbitrage condition that is fundamental in stochastic asset pricing in finance.

Contents
• Financial Mathematics in a non stochastic framework.

• Elementary probability calculus.

• Applications of Financial Mathematics and probability to portfolio selection and to life insurance policy pricing.

Texts
Pressacco F., Stucchi P. (2007) “Elementi di Matematica Finanziaria”, CEDAM

Notes by the teacher on probability.

Further insights:

Cacciafesta F. (last edition) “Lezioni di matematica finanziaria classica e moderna”, Giappichelli

Edited by Miani S. (last edition) “I prodotti assicurativi”, Giappichelli, 2nd chapter by Pressacco F. and Ziani L.