Ateneo - UPO

The course covers selected statistical methods and basic elements of financial mathematics relevant to a legal education.

Specifically, it addresses descriptive statistics, the fundamentals of probability theory, and decision-making under uncertainty; essential financial techniques such as compounding and discounting cash flows, the valuation of bonds and annuities, and the construction of loan amortization schedules.

Mandatory reading materials will be made available by the module instructors on their respective DIR course pages.

Useful reference texts include:
Mecatti, F. Statistica di Base. Come, quando e perché. 3/ED (2022). Milano. McGraw-Hill.
Mauro D’Amico, Lorenzo Peccati. Metodi matematici, statistici e finanziari per giuristi (7a edizione) (2016). Milano.

The course aims to provide a foundational understanding of statistical and probabilistic analyses, as well as core financial operations along with their underlying mathematical tools.

The primary objective of the course is to ensure students achieve an adequate grasp of the results obtained and the potential of the tools presented as legal expertise. From this standpoint, applying these methodologies and using the proposed tools are intended as means to achieve the learning outcomes, rather than ends in themselves.

The course is worth 6 ECTS credits (CFU), corresponding to 45 hours of direct instruction divided into two modules. Overall, it includes approximately 30 hours of lecture-based instruction (DE) and 15 hours of interactive instruction (DI). The split between the two modes is flexible and may vary across individual lessons.

Basic algebra.

Lectures and practical exercises.

Attendance is not mandatory but is strongly recommended. Students with physical disabilities, Learning Disabilities or Special Education Needs can request specific services and tools via the Staff Sviluppo e Coordinamento Carriere e Servizi alle Studentesse e agli Studenti, consulting the University webpage: https://www.uniupo.it/en/services/servicesstudents-physical-or-learning-disabilities. Students with disabilities, learning disabilities or special education needs, once they have contacted the University Staff, can refer to the tutor in charge of the course to define the examination modalities, concerning academic aspects.

The exam consists of a compulsory written test, with a possible confirmation oral exam, and an optional oral exam.

The written test consists of 8 multiple-choice questions (4 related to Quantitative Methods 1 and 4 related to Quantitative Methods 2). Each question has 5 possible answers, of which only one is correct, and the test must be completed within 90 minutes. Each answer provided must be accompanied by an explanation/justification. Each correct answer that is properly justified is worth one point. Each incorrect answer, unanswered question, or answer provided without justification or with an incorrect justification receives 0 points.

The written test has a maximum score of 26/30 (8 correct answers) and is considered passed only if the student obtains at least two correct answers in both Quantitative Methods 1 and Quantitative Methods 2. The written test is concluded only after the possible confirmation oral exam, if the Professor deems that clarification on the submitted work is necessary. Failure to attend the confirmation oral exam results in an insufficient grade for the written test. The questions cover the course topics and aim to verify the skills achieved in applying acquired knowledge to solve problems.

The optional oral exam is available to students who obtain a passing grade (greater than or equal to 20/30) in the written test and may result in a change of the written-test score ranging from −3 to +4 points. Students must first demonstrate the ability to identify any errors made in the written exam, pinpointing the correct approaches and providing a clear explanation. In addition, a score of up to 2 points requires demonstrating a sufficiently broad knowledge and understanding of the course contents that, in particular, enables the student to establish connections between different topics. To achieve a score of 3 to 4 points, students must be able to independently apply their knowledge and understanding of the course content to engage in an in-depth discussion on critical aspects related to the subjects covered, using clear and rigorous language.

The final grade is the sum of the grades obtained in the written test and, if taken, the oral exam, up to a maximum of 30/30 with honors. The awarding of honors is subject to the student’s ability to independently solve some questions (exercises or more theoretical questions) of above-average difficulty.

Further details regarding the exam procedures are published on the course DIR page

Module 1:
Population, sample, variable, modality. Frequency distributions and their representations. Summary indicators: averages and measures of variability. Double entry tables and conditional distributions. Linear regression function: calculation of coefficients and measurement of the goodness of fit. Elements of probability calculus. Conditional probabilities and Bayes formula. Samples and estimates (point and interval). Testing of statistical hypotheses: I and II type errors, level and power. Decision rules and p-value.

Module 2:
Financial operations: amounts, maturities, principal, amount, interest, interest rate, discount, discount rate, nominal value, present value, capitalisation and discounting (and factors). Financial regimes: simple interest, simple discount, compound interest, compound discount, equivalent rates, commercial discount. Bonds: zero coupon bonds and coupon bonds. Classification and evaluation of anticipated and deferred financial annuities. Perpetual annuities (hints). Forms of repayment of a loan: general. Amortization of a loan: elementary setup and financial setup.