Knowledge and understanding: At the end of the course, students must have acquired the knowledge of a basic set of mathematical tools, relative to economy and finance of insurance. Applying knowledge and understanding: At the end of the course, students must be able to apply the mathematical methods developed in the course to the solution of problems, and to model using mathematical language economic and financial problems relative to insurance theory. Making judgments: At the end of the course, students must be able to create links among notions acquired during the course and to tackle economic-business problems through the use of logical and formal mathematical tools. Communication skills: At the end of the course, students must acquire an ability to communicate clearly and effectively the acquired knowledge. Learning skills: At the end of the course, students must have developed good learning skills, which allow them to independently apply the knowledge acquired during their studies.

The course will widely use the notions of Economics, Mathematics, Probability Calculus.

Preferences and utility functions: 1) Preorders and orders; 2) total preorders and weak orders; 3) Lower and upper sections in a totally preordered set; 4) increasing and order-preserving functions on a preordered set; 5) Utility functions on a totally preordered set: 6) characterization of the existence of a utility function on a totally preordered set; Money lotteries and certainty equivalents: 1) Definition of money lottery; 2) total preorders on the set of all money lotteries; 3) expectation, risk premium and certainty equivalent; 4) Characterization of the existence of a certainty equivalent .Insurance and risk attitudes: 1) Basic concepts relative to insurance; 2) risk aversion, neutrality and propensity; 3) isoprofit lines; 4) profitability of insurance and risk aversion; 5) insurance for a risk-neutral, respectively, a risk-averse, individual Expected utility for preferences over money lotteries. Von Neumann Morgenstern Theorem. 1) Definition of expected utility; 2) St. Petersburg and Allais paradoxes; 3) zero-utility premium principle; 4) independence and continuity under risky conditions; 5) Existence of a linear utility functional: von Neumann and Morgenstern theorem with proof; 6) simple probability measures and expected utility. Mean-variance portfolio choice and multi-objective optimization: 1) Basic concepts relative to portfolio theory; 2) Markowitz portfolio selection problem: theorem with proof; 3) multi-objective optimization; 4) Efficient frontier; 5) Capital asset pricing model with applications.

Book preprint a cura del docente. Giacomo Bonanno, The Economics of Uncertainty and Insurance, University of California, Davis.

Preferences and utility functions: 1) Preorders and orders; 2) total preorders and weak orders; 3) Lower and upper sections in a totally preordered set; 4) increasing and order-preserving functions on a preordered set; 5) Utility functions on a totally preordered set: 6) characterization of the existence of a utility function on a totally preordered set; Money lotteries and certainty equivalents: 1) Definition of money lottery; 2) total preorders on the set of all money lotteries; 3) expectation, risk premium and certainty equivalent; 4) Characterization of the existence of a certainty equivalent .Insurance and risk attitudes: 1) Basic concepts relative to insurance; 2) risk aversion, neutrality and propensity; 3) isoprofit lines; 4) profitability of insurance and risk aversion; 5) insurance for a risk-neutral, respectively, a risk-averse, individual Expected utility for preferences over money lotteries. Von Neumann Morgenstern Theorem. 1) Definition of expected utility; 2) St. Petersburg and Allais paradoxes; 3) zero-utility premium principle; 4) independence and continuity under risky conditions; 5) Existence of a linear utility functional: von Neumann and Morgenstern theorem with proof; 6) simple probability measures and expected utility. Mean-variance portfolio choice and multi-objective optimization: 1) Basic concepts relative to portfolio theory; 2) Markowitz portfolio selection problem: theorem with proof; 3) multi-objective optimization; 4) Efficient frontier; 5) Capital asset pricing model with applications.

Lectures and traditional classroom tutorials will be provided. Besides, online teaching activity will be available on Moodle

We shall be based on notions furnished in the courses of Elementi di Economia, Matematica per l'economia, Calcolo delle probabilità.

The examination consists of an oral exam with open questions, that aims to test a sound knowledge and comprehension of the arguments presented during the lessons. The students have to prove their comprehension of the fundamental concepts explained in the course and their ability of connecting the different topics; moreover, they have to be able to present the acquired knowledges clearly.

3. Good health and well-being 4. Quality education 9. Decent work and economy growth