Ateneo - UPO

Introduction to decision-making problems: Linear programming techniques and applications; decisions under risk: expected utility, certainty equivalent, risk premium, attitude towards risk, mean-variance criterion.

- Lecture notes by the teacher.

Recommended readings:
- Bellenzier L., Grassi R., Stefani S., Torriero A., Metodi quantitativi per il Management, Esculapio, 2012. (Chapter 1, Chapter 2 up to Section 2.4 included)
- Martello S., Speranza M.G:, Ricerca Operativa per l'Economia e l'Impresa, Esculapio, 2012 (Chapters 1 and 2 just reading, Chapter 3, Chapter 4).
- Castellani G., De Felice M., Moriconi F., Manuale di Finanza II, Il Mulino, 2005 (Chapter 1, Chapter 2 except Section 2.5, Chapter 3 except Section 3.2).

Achieving a full understanding of basic mathematical knowledge related to the resolution and discussion of the results of a linear programming problem. Acquisition of knowledge related to some basic criteria of individual choice under uncertainty, and judgment in choosing and using analysis tools suitable for solving simple problems. Development of the ability of communicating in a sufficiently rigorous way the logicdeductive way of problem solving.

Differential calculus for real functions of one and several real variables. Linear Algebra (vector, matrices, linear systems) and introductory descriptive statistics.
The exam of Mathematical Methods 1 is compulsory. It is recommended to take the exams of Mathematical Methods 2 and Statistics.

Lectures, tutorials with also digital supports: use of the DIR platform for the use of support materials and the WOOCLAP platform for discussion in the classroom.

Any useful information on the course and supplementary didactic resources can be found on the web page of the course at the URL: https://dir.uniupo.it/. 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/services- students-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 is oral and consists of some questions / exercises designed to assess: • the knowledge, understanding and ability to apply the techniques of analysis and discussion of the results of a linear programming problem; • the knowledge, understanding and ability to apply some criteria of individual choice to real problems under risk conditions, together with the ability to present the results achieved with an appropriate and rigorous technical language. There are 7 exam sessions in each solar year but students can enroll no more than three times, at their own choice. It is mandatory to register for the exam through the students portal: once the three exam participations have been reached, including withdrawals and refusals, the system will not allow further registrations. For attending students, a partial test and a final exam are available in addition to the official exams: details are given on the course DIR page.

Resource allocation decisions under certainty. Linear Programming: real-world problems modelling, variables, constraints, objective function, the feasible region, solutions. Solution methods: graphical analysis (two variables), algebraic method, iterative methods; implementation with Excel. Sensitivity analysis. Introduction to decision-making problems. Preference and indifference relations and their properties. Criterion of expected value maximization (MVA), fair price, applications to the theory of insurance. Mean-variance criterion. Expected utility theory: compound lotteries, axioms of rationality, representation theorem of Von Neumann - Morgenstern. Principle of maximization of expected utility. Certainty equivalent: definition and examples. Attitude towards risk. The risk premium. Estimation of the utility function. Attitudes towards risk and the concavity of the utility function. Measure of risk aversion. Quadratic approximation of an utility function. Mean-variance criterion. Applications to the insurance and portfolio selection.

The expected results related to a medium level of preparation are: -Discrete knowledge of the main mathematical notions and solving methods of linear (PL); knowledge of some important decision criteria under risk conditions. - Good ability to formalize, solve and analyze the solutions, both graphically, both with the simplex tables, and with the spreadsheet, of a problem of PL in two variables; sufficient ability to solve problems of choice with the criterion of maximization of the expected value, the criterion of mean-variance and the criterion of the maximization of the expected utility. -Maturation of a discrete judgment in the choice and use of calculation tools suitable for the resolution of the aforementioned problems. -Sufficient ability to communicate in a clear and rigorous way the logical-deductive paths followed in addressing the proposed problems.