Statistics, Economics, Finance and Insurance

Educational objectives

Learning goals.
Knowledge and comprehension of the basic concepts and techniques of linear algebra and of analytic geometry of the plane and the space and ability to apply them to the study and resolution of simple problems also in the context of other courses.

Knowledge and understanding.
Good theoretical and practical knowledge of matrices, linear systems and other fundamental notions of linear algebra and ability to understand these issues also in the context of other courses.

Applying knowledge and understanding.
Ability to use the acquired skills for solving simple problems on matrices, linear systems and other fundamental notions of linear algebra, also for their use required in other courses.

Making judgements.
Good ability to recognize, frame and set out the resolution of simple problems on matrices, linear systems and other fundamental notions of linear algebra, possibly selecting appropriately among the methods learned.

Communication skills.
Good presentation skills of basic concepts and techniques of linear algebra as well as solution methods to simple problems.

Learning skills.
Good learning ability of mathematical issues in other courses, by virtue of the comprehension of the logical-deductive character of the discipline.

Educational objectives

Learning goals.
The main educational goal of this course is that students learn the fundamental concepts of exploratory statistics, both from a theoretical point of view and for what concerns practical applications.

Knowledge and understanding.
After attending this course students know and understand the main concepts of exploratory statistics (e.g. characteristics of a simple distribution, relationships between variables) and the main methods to summarize and quantitatively evaluate them (graphical representations, tables, statistical indices).

Applying knowledge and understanding.
At the end of the course students are able to use the technical tools for building the most important statistical indices and for studying their properties.
Consequently they can deal with the practical issues involved in the application of these methods for exploratory data analysis and they can provide the interpretation of the results.

Making judgements.
Students develop their critical sense by applying methods of exploratory data analysis to real data sets, especially through the choice and the comparison of alternative solutions to the same problem.
They are able to discriminate and critically interpret the results of the analysis.

Communication skills.
Students acquire the technical language of statistics, that has to be used conveniently in the examinations and that constitutes a solid base for the whole course of their studies.
Communications skills are stimulated during the lectures and developed also through homeworks and other group activities.

Learning skills.
Students that pass the exam are familiar with theoretical and practical tools for exploratory data analysis and therefore they have acquired a technical language and a method that allow them to tackle with the future steps of their educations, starting from the more advanced courses in statistics until the construction of their professional profile.

Educational objectives

Learning goals.
The main goal of the course is to give basic knowledge of computer science, to provide the tools for understanding what a computational problem is and which kind of logical reasoning may lead to its solution.
In the meantime we want to work on programming skills (e.g. Python programming) and on querying relational databases.

Knowledge and understanding.
At the end of the course the students will know what an algorithm is, what difference exists between data and its representation, how to reason using abstraction techniques.
They will be able to code in Python to solve new problems, using as well the theoretical knowledge of algorithm analysis.
They will know how relational databases are organized, and will learn the SQL language, useful to query them.

Applying knowledge and understanding.
Learing about the theory of algorithms and a programming language allows the students to solve new computational problems in a flexible way.

Making judgements.
Algorithmic thinking (also called computational thinking), which is trained by the students during this course, gives tools and techniques for rigorous and non-ambiguous analysis of problems, using only relevant information.

Communication skills.
Students learn the technical and scientific language of computer science, which must be appropriately used in written and viva exams.
Moreover writing code documentation trains the students to explain their work with clarity.

Learning skills
The course show the students new concepts (e.g. programming, theory of algorithms).
The effort required to understand and apply these concepts allows them to study and evaluate new techniques and programming languages.

Educational objectives

Knowledge and understanding.
Good theoretical and practical knowledge of differential calculus, integration, power series (real functions of one real variable).
Ability to understand these issues also in the context of other courses.

Applying knowledge and understanding.
Ability to use the acquired skills for solving simple problems and for their use required in other courses.

Making judgements.
Good ability to recognize, frame and set out the resolution of simple problems, selecting appropriately among the methods learned.

Communication skills.
Good presentation skills of basic concepts and techniques of Calculus.

Learning skills.
Good learning ability of mathematical issues in other courses, by virtue of the comprehension of the logical-deductive character of the discipline.

Educational objectives

Learning goals
Aim of the course is to offer a general introduction to economics, considered both as a social discipline which helps us to understand the economic events of the society we live in and as a “technical” discipline, required to a larger or lesser extent in many work activities.

Knowledge and understanding
Knowledge of the basic concepts and of the main theories elaborated in the economic field .Historical perspective and awareness of the existence of different interpretative positions for what concerns economics.

Applying knowledge and understanding
At the end of the course students are able to formalize real economic problems and to apply the specific methods of the discipline to solve them. They are also able to deal with the most important economic models (both microeconomic and macroeconomic) and to apply the learned methods to models to be developed in the future. Finally, they are able to link methods to short-term data.

Making judgements
Students develop critical skills through the application of the same methodology to a wide range of economic models, which are affected by different theoretical approaches.

Communication skills
Students, through the study, acquire the technical-scientific language of the discipline, which must be appropriately used both in written and oral exams.

Learning skills
Students who pass the exam have learned a method of analysis that allows them to tackle the study of more complex models (both microeconomic and macroeconomic) in advanced courses in economics.

Educational objectives

Learning goals
The course aims, first, to achieve the student the basics of business law in the context of the broader relationship between the concepts of economics and law, particularly as regards the discipline of the company, controls and the internal market.The terms provided are intended to make students able to cope independently and detailed issues, including whether in contract, connected to action of the company, whe1ther publicly or privately, in a free market.It is expected that the student demonstrates the ability to use the knowledge gained to solve specific problems that characterize the economic and legal context in which the company is to operate.

Knowledge and understanding

Applying knowledge and understanding

Making judgements

Communication skills

Learning skills

Educational objectives

Objectives
This course aims to give students a solid grounding in statistical terminology and to acquaint them with the typical linguistic features and characteristics of standard statistical presentations and publications.

Skills studied
Proceeding from the elementary skills of interpreting and describing tables and graphs, the course will focus on expository texts ,so as to enable the students gain facility in describing the statistical methods underlying reported data. It is hoped that by the end of the course, the students, with reference to the publications of the Istitutonazionale di statistica , will be able to make competent statistical presentations in English on the economic and social realities of Italy and to respond to questions and requests for clarification thereon.

Educational objectives

Knowledge and understanding.
Good theoretical and practical knowledge of differential calculus and integration for functions of several real variables. Ability to understand these issues also in the context of other courses.

Applying knowledge and understanding.
Ability to use the acquired skills for solving simple problems and for their use required in other courses.

Making judgements.
Good ability to recognize, frame and set out the resolution of simple problems, selecting appropriately among the methods learned.

Communication skills.
Good presentation skills of basic concepts and techniques of Mathematical analysis.

Learning skills.
Good learning ability of mathematical issues in other courses, by virtue of the comprehension of the logical-deductive character of the discipline.

Educational objectives

Learning Goals
The course tackles the subjects and problems of the classical Financial Mathematics and aims at providing theoretical notions and operational capacities that enable to solve the main financial problems in certainty conditions that arise in business and financial markets.

Knowledge and understanding
The student will learn, from a theoretical and operational point of view, the main financial schemes, tools for the assessment of income and for amortization schedules, the main criteria for financial decisions under certainty and, the tools to estimate the term structure of interest rates and financial immunization.

Applying knowledge and understanding
Each theoretical concept will be applied to real cases. Students will be assessed according to their ability to solve specific problems

Making Judgements
Each student will be required to download real market data and build the term structure of interest rates or a repayment of loan plan in order to be able to validate his/her ability to do so

Communication Sklls
Each student will be required to present the application of studied methodologies to solve a real problem

Learning Skills
The learned concepts will be tested having each student to undertake a final exam

Educational objectives

Learning goals

General goals.
The primary educational goal of teaching is to learn the main concepts and methods of probability.
Students must also be able to apply the above methods and be able to interpret the results that derive from their solution.

Knowledge and understanding.
After attending the course the students know and understand the main probabilistic concepts (events, random variables, probability distributions)

Applying knowledge and understanding.
At the end of the course the students are able to formalize real problems and to solve them by applying the specific methods of the discipline.

Making judgements.
Students develop critical skills through the application of probabilistic theory.

Communication skills.
Students, through the study and performance of practical exercises, acquire the technical-scientific language of the discipline, which must be used appropriately in both the intermediate and final written tests and in the oral tests.

Learning skills.
Students who pass the exam have learned a method of analysis that allows them to tackle the subsequent teachings of statistical-probabilistic area.

Educational objectives

Learning goals

General goals.
The primary educational goal of teaching is to learn the main concepts and methods of probability.
Students must also be able to apply the above methods and be able to interpret the results that derive from their solution.

Knowledge and understanding.
After attending the course the students know and understand the main probabilistic concepts (events, random variables, probability distributions)

Applying knowledge and understanding.
At the end of the course the students are able to formalize real problems and to solve them by applying the specific methods of the discipline.

Making judgements.
Students develop critical skills through the application of probabilistic theory.

Communication skills.
Students, through the study and performance of practical exercises, acquire the technical-scientific language of the discipline, which must be used appropriately in both the intermediate and final written tests and in the oral tests.

Learning skills.
Students who pass the exam have learned a method of analysis that allows them to tackle the subsequent teachings of statistical-probabilistic area.

Educational objectives

Learning goals

General goals.
The primary educational goal of teaching is to learn the main concepts and methods of probability.
Students must also be able to apply the above methods and be able to interpret the results that derive from their solution.

Knowledge and understanding.
After attending the course the students know and understand the main probabilistic concepts (events, random variables, probability distributions)

Applying knowledge and understanding.
At the end of the course the students are able to formalize real problems and to solve them by applying the specific methods of the discipline.

Making judgements.
Students develop critical skills through the application of probabilistic theory.

Communication skills.
Students, through the study and performance of practical exercises, acquire the technical-scientific language of the discipline, which must be used appropriately in both the intermediate and final written tests and in the oral tests.

Learning skills.
Students who pass the exam have learned a method of analysis that allows them to tackle the subsequent teachings of statistical-probabilistic area.

Educational objectives

Learning goals.
The main learning goal for students is the knowledge of principles and methods of Statistical inference.
Students must be able to apply the main inferential techniques and to interpret the results of their use on real data.

Knowledge and understanding.
Students acquire knowledge and understanding of the most important inferential problems (point estimation, interval estimation, hypothesis testing) and of the main methods for solving these problems (maximum likelihood estimates, confidence intervals, parametric tests).

Applying knowledge and understanding.
After the attendance of this course, students will be able to formalize real problems into inferential problems and to apply appropriate inferential methods.
They will be able to use the main parametric models and to apply methods to models not considered in classwork.
They will also be able to apply inferential techniques ti real data and to interpret them.

Making judgements.
Students improve judgements skills by applying inferential methods to a wide range of statistical models.
Their skills will be improved by using and comparing different methods to the same problems and by applying these methods to real data.

Communication skills
Students will acquire the scientific language of Statistics, that will be used in written and oral tests.
Communication skills will be enhanced also by group work.

Learning skills.
Students will acquire the fundamental knowledge needed to study formal inferential properties of more complex models in more advanced classes.

Educational objectives

Learning goals
Working knowledge of the main models of economic dynamics

Knowledge and understanding
Upon succesfull completion of the course, students will be able to analyse actual economic problems in terms of competing theories and models.

Applying knowledge and understanding
Upon succesfull completion of the course, students will be able to understand the explicit and implicit hypotheses informing the main economic policy proposals in the current debate.

Making judgements
The course is explicitly based on the principle of methodological and theoretical pluralism. Students will be introduced to at least two competing models for each economic problem considered, and will understand the criteria with which to personally choose their favourite interpretation

Communication skills
Through study and hands-on sessions, students will become proficient in the jargon and technical language of the discipline, which they must use in both written and oral examinations.

Learning skills
Students that succesfully complete the course will have learnt a method of analysis that will allow them to tackle and understand the main economic issues of today, both in subsequent economic courses and in the fruition and participation to the public debate

Educational objectives

Learning goals.
The main learning goal for students is the knowledge of principles and methods of actuarial mathematics, both of life and non life insurance.
Students must be able to apply the main actuarial models and to interpret the results of their use on real data.

Knowledge and understanding.
Students acquire knowledge and understanding of the most important problems of actuarial mathematics (probabilistic models, premium principles, reserves, ecc.) and of the main methods for solving these problems (variance principle, chain ladder method, Homans formula, ecc.).

Applying knowledge and understanding.
After the attendance of this course, students will be able to formalize real problems and to apply appropriate actuarial models.
They will also be able to apply actuarial models to real data and to interpret them.

Making judgements.
Students improve judgements skills by applying actuarial models to a wide range of insurance products.
Their skills will be improved by using and comparing different methods to the same problems and by applying these methods to real data.

Communication skills
Students will acquire the scientific language of Actuarial mathematics, that will be used in written and oral tests.
Communication skills will be enhanced also by group work.

Learning skills.
Students will acquire the fundamental knowledge needed to study formal actuarial properties of more complex models in more advanced classes.

Educational objectives

Learning goals.
The main goal of the course is the acquisition of the fundamental statistical tools for the analysis of multivariate data and their use in real applications.
At the end of the course, the student should be able to formalize the statistical goal of a real case study, to develop a strategy of analysis by selecting appropriate methods, to apply the methodology and derive the correct conclusions by producing a (short) technical report which selects and collects the main the results.

Knowledge and understanding.
When completing the course, students will have learnt the main issues and essential concepts of multivariate and multidimensional analysis (for example, dependence, dimension reduction, classification) and the standard methodologies to face and handle such problems (such as, linear regression, PCA and cluster analysis).

Applying knowledge and understanding.
When completing the course, students will be able to formalize a multivariate statistical problem and select the appropriate methodologies to face such a problem.
Moreover, they will have the basic skills to explain possible choices, to make comparisons and to assess assumptions and applicability.
Finally, they will be able to apply the methods to real data and interpret the results.

Making judgements.
Students develop the critical thinking by applying the methodologies learnt which they will be able to use in autonomy by means of statistical software.
The capability to process data and produce the output by themselves reveals the autonomy in analyzing, making judgements necessary to make choices and comparisons taking into considerations theoretical criteria.
In addition, students will learn to critically interpret the results obtained in real applications.

Communication skills.
By processing data and making short technical reports, students will learn the correct use of the technical language which is required in both coursework and final exam.
Special attention is given to the skill of communicating results to non-specialists by using a rigorous but understandable language.

Learning skills
Students passing the exam have learnt:
a) the theoretical background in advanced statistics to possibly pass to a Second Cycle Degree in either Statistics or Applied Statistics;
b) the tools to develop and build a strategy of analysis in autonomy when analyzing data which are necessary either to tackle a job or to continue the Programme of Study.

Educational objectives

Knowledge and understanding.
Students who have attended the course of stochastic processes will have a general understanding of the modern theory of stochastic processes including point processes, martingales, stochastic calculus with respect to the Brownian motion. Some parts of the program have an advanced character and involve fractional Brownian motion and the interplay between partial differential equations and diffusion processes.

Ability of applying knowledge and understanding.
The part of the course concerning stochastic calculus make the students capable of applying the concepts and techniques to the main models of finance (Black and Scholes, Vasichek and others). The Feynman-Kac functional permits the students to have at hand a flexible and powerful tool for many specific situations.

Autonomous judgement.
The course is presented with the aim of inserting the subject in the framework of modelling random phenomena in finance, economics and physics. Each part of the program is presented both on an intuitive and rigorous basis letting the student foresee further developments.

Communication skills.
The study of many probabilistic concepts and techniques gives the possibility of acquiring a rigorous terminology and a method of proving results according to the scheme assumption, proof, conclusion, interpretation of the results.

Learning skills.
The style of lesson is such that the student must learn to learn new concepts and acquire new knowledge and it aims at stimulating the curiosity about all possible applications and interactions between scientific fields.

Educational objectives

Learning goals aims and objectives
Critical understanding of capital market modeling, of pricing models and related financial problems; proficiency in the use of quantitative techniques and evaluation criteria for financial choices; ability to collect, interpret and select data characterising financial contracts and markets, knowledge of financial jargon and relevant linguistic correspondences (Italian-English).

Knowledge and understanding.
Base elements of Calculus, Probability, and Statistics.

Applying knowledge and understanding.
Ability to apply quantitative methods to portfolio selection, to the valuation of derivatives and financial contracts, to the analysis of financial markets; critical tools for reading and interpreting contracts and financial market conditions.

Making judgements
Critical tools for the evaluation of literature of the field.

Communication skills.
The studens will have to be able to talk - with knowledge and insights- on the problem of portfolio selection and on base elements of financial markets.

Learning skills.
The student will be able to apply mathematical and software tools to Portfolio selection problem and base financial markets.

Educational objectives

Learning goals.
The main objective of this course is to provide the knowledge a life actuary requires to operate accordingly to the Solvency II directive.
It will teach students to understand valuation techniques for with profit, unit linked, and index linked policies; methods of life best-estimate, SCR, and cost-of-capital calculation according to the Solvency II directive.

Knowledge and understanding
At the end of the course, students will know and understand the principles of life market-consistent evaluation (best estimate).
They will be able to comprehend the standard formula SCR calculation criteria. They will be familiar with the main validation tests.
They will understand profit test reports.

Applying knowledge and understanding
At the end of the course, students will have acquired the ability to apply best estimate and SCR calculation methods to real cases.
Additionally, they will be able to evaluate with profit policies, in an Asset Liabilities Management setting, using segregated fund accounting rules.
They will know how to realize the accuracy, robustness, market consistency, and "martingale" tests required by regulation for the economic scenarios generator.
Using these abilities, they will plan profit test reports.

Making judgements
Students will be able to critically interpret the outcomes of models, by varying the contractual parameters and/or the model parameters.

Communication skills.
The students acquire the knowledge of industry jargon and of the relevant linguistic correspondences (Italian-English).

Learning skills.
Students who pass the final exam will have acquired the methods and knowledge necessary to operate as life actuaries, with a special regard for life technical provition and SCR according to the Solvency II directive.
These skills will allow them access to the State Examination to the Actuarial Profession.

Educational objectives

Course objectives – The course aims to provide: 1. the fundamental principles of the mean-variance approach to portfolio selection; 2. approaches to asset-liability management of financial portfolios subject to interest rate risk.
Expected achievements – The course should allow the students to address the main problems of portfolio management.

Educational objectives

The final exams consists of writing, presenting and discussing a thesis, developed autonomously by the students, which illustrates in a coherent and detailed manner the problem tackled during the practical training and all the activities carried out to develop its solution.

Educational objectives

Learning goals.
Knowledge and comprehension of the basic concepts and techniques of linear algebra and of analytic geometry of the plane and the space and ability to apply them to the study and resolution of simple problems also in the context of other courses.

Knowledge and understanding.
Good theoretical and practical knowledge of matrices, linear systems and other fundamental notions of linear algebra and ability to understand these issues also in the context of other courses.

Applying knowledge and understanding.
Ability to use the acquired skills for solving simple problems on matrices, linear systems and other fundamental notions of linear algebra, also for their use required in other courses.

Making judgements.
Good ability to recognize, frame and set out the resolution of simple problems on matrices, linear systems and other fundamental notions of linear algebra, possibly selecting appropriately among the methods learned.

Communication skills.
Good presentation skills of basic concepts and techniques of linear algebra as well as solution methods to simple problems.

Learning skills.
Good learning ability of mathematical issues in other courses, by virtue of the comprehension of the logical-deductive character of the discipline.

Educational objectives

Learning goals.
The main educational goal of this course is that students learn the fundamental concepts of exploratory statistics, both from a theoretical point of view and for what concerns practical applications.

Knowledge and understanding.
After attending this course students know and understand the main concepts of exploratory statistics (e.g. characteristics of a simple distribution, relationships between variables) and the main methods to summarize and quantitatively evaluate them (graphical representations, tables, statistical indices).

Applying knowledge and understanding.
At the end of the course students are able to use the technical tools for building the most important statistical indices and for studying their properties.
Consequently they can deal with the practical issues involved in the application of these methods for exploratory data analysis and they can provide the interpretation of the results.

Making judgements.
Students develop their critical sense by applying methods of exploratory data analysis to real data sets, especially through the choice and the comparison of alternative solutions to the same problem.
They are able to discriminate and critically interpret the results of the analysis.

Communication skills.
Students acquire the technical language of statistics, that has to be used conveniently in the examinations and that constitutes a solid base for the whole course of their studies.
Communications skills are stimulated during the lectures and developed also through homeworks and other group activities.

Learning skills.
Students that pass the exam are familiar with theoretical and practical tools for exploratory data analysis and therefore they have acquired a technical language and a method that allow them to tackle with the future steps of their educations, starting from the more advanced courses in statistics until the construction of their professional profile.

Educational objectives

Learning goals.
The main goal of the course is to give basic knowledge of computer science, to provide the tools for understanding what a computational problem is and which kind of logical reasoning may lead to its solution.
In the meantime we want to work on programming skills (e.g. Python programming) and on querying relational databases.

Knowledge and understanding.
At the end of the course the students will know what an algorithm is, what difference exists between data and its representation, how to reason using abstraction techniques.
They will be able to code in Python to solve new problems, using as well the theoretical knowledge of algorithm analysis.
They will know how relational databases are organized, and will learn the SQL language, useful to query them.

Applying knowledge and understanding.
Learing about the theory of algorithms and a programming language allows the students to solve new computational problems in a flexible way.

Making judgements.
Algorithmic thinking (also called computational thinking), which is trained by the students during this course, gives tools and techniques for rigorous and non-ambiguous analysis of problems, using only relevant information.

Communication skills.
Students learn the technical and scientific language of computer science, which must be appropriately used in written and viva exams.
Moreover writing code documentation trains the students to explain their work with clarity.

Learning skills
The course show the students new concepts (e.g. programming, theory of algorithms).
The effort required to understand and apply these concepts allows them to study and evaluate new techniques and programming languages.

Educational objectives

Knowledge and understanding.
Good theoretical and practical knowledge of differential calculus, integration, power series (real functions of one real variable).
Ability to understand these issues also in the context of other courses.

Applying knowledge and understanding.
Ability to use the acquired skills for solving simple problems and for their use required in other courses.

Making judgements.
Good ability to recognize, frame and set out the resolution of simple problems, selecting appropriately among the methods learned.

Communication skills.
Good presentation skills of basic concepts and techniques of Calculus.

Learning skills.
Good learning ability of mathematical issues in other courses, by virtue of the comprehension of the logical-deductive character of the discipline.

Educational objectives

Learning goals.
An introduction to the basic skills of empirical economic analysis

Knowledge and understanding.
After taking the course the students know and understand the main problems in measuring economic variables and the methods to be used to solve them.

Applying knowledge and understanding.
After taking the course the students know how to solve the main problems in measuring economic variables.

Making judgements.
Students develop their critical skills through the analysis of real datasets.

Communication skills.
Students acquire the technical language, which must be used both in the written exam and in the individual project.

Learning skills.
Students passing the exam have acquired the ability to read and realise basic empirical economic studies.

Educational objectives

Learning goals
Aim of the course is to offer a general introduction to economics, considered both as a social discipline which helps us to understand the economic events of the society we live in and as a “technical” discipline, required to a larger or lesser extent in many work activities.

Knowledge and understanding
Knowledge of the basic concepts and of the main theories elaborated in the economic field .Historical perspective and awareness of the existence of different interpretative positions for what concerns economics.

Applying knowledge and understanding
At the end of the course students are able to formalize real economic problems and to apply the specific methods of the discipline to solve them. They are also able to deal with the most important economic models (both microeconomic and macroeconomic) and to apply the learned methods to models to be developed in the future. Finally, they are able to link methods to short-term data.

Making judgements
Students develop critical skills through the application of the same methodology to a wide range of economic models, which are affected by different theoretical approaches.

Communication skills
Students, through the study, acquire the technical-scientific language of the discipline, which must be appropriately used both in written and oral exams.

Learning skills
Students who pass the exam have learned a method of analysis that allows them to tackle the study of more complex models (both microeconomic and macroeconomic) in advanced courses in economics.

Educational objectives

Objectives
This course aims to give students a solid grounding in statistical terminology and to acquaint them with the typical linguistic features and characteristics of standard statistical presentations and publications.

Skills studied
Proceeding from the elementary skills of interpreting and describing tables and graphs, the course will focus on expository texts ,so as to enable the students gain facility in describing the statistical methods underlying reported data. It is hoped that by the end of the course, the students, with reference to the publications of the Istitutonazionale di statistica , will be able to make competent statistical presentations in English on the economic and social realities of Italy and to respond to questions and requests for clarification thereon.

Educational objectives

Knowledge and understanding.
Good theoretical and practical knowledge of differential calculus and integration for functions of several real variables. Ability to understand these issues also in the context of other courses.

Applying knowledge and understanding.
Ability to use the acquired skills for solving simple problems and for their use required in other courses.

Making judgements.
Good ability to recognize, frame and set out the resolution of simple problems, selecting appropriately among the methods learned.

Communication skills.
Good presentation skills of basic concepts and techniques of Mathematical analysis.

Learning skills.
Good learning ability of mathematical issues in other courses, by virtue of the comprehension of the logical-deductive character of the discipline.

Educational objectives

Learning goals

General goals.
The primary educational goal of teaching is to learn the main concepts and methods of probability.
Students must also be able to apply the above methods and be able to interpret the results that derive from their solution.

Knowledge and understanding.
After attending the course the students know and understand the main probabilistic concepts (events, random variables, probability distributions)

Applying knowledge and understanding.
At the end of the course the students are able to formalize real problems and to solve them by applying the specific methods of the discipline.

Making judgements.
Students develop critical skills through the application of probabilistic theory.

Communication skills.
Students, through the study and performance of practical exercises, acquire the technical-scientific language of the discipline, which must be used appropriately in both the intermediate and final written tests and in the oral tests.

Learning skills.
Students who pass the exam have learned a method of analysis that allows them to tackle the subsequent teachings of statistical-probabilistic area.

Educational objectives

Learning goals

General goals.
The primary educational goal of teaching is to learn the main concepts and methods of probability.
Students must also be able to apply the above methods and be able to interpret the results that derive from their solution.

Knowledge and understanding.
After attending the course the students know and understand the main probabilistic concepts (events, random variables, probability distributions)

Applying knowledge and understanding.
At the end of the course the students are able to formalize real problems and to solve them by applying the specific methods of the discipline.

Making judgements.
Students develop critical skills through the application of probabilistic theory.

Communication skills.
Students, through the study and performance of practical exercises, acquire the technical-scientific language of the discipline, which must be used appropriately in both the intermediate and final written tests and in the oral tests.

Learning skills.
Students who pass the exam have learned a method of analysis that allows them to tackle the subsequent teachings of statistical-probabilistic area.

Educational objectives

Learning goals

General goals.
The primary educational goal of teaching is to learn the main concepts and methods of probability.
Students must also be able to apply the above methods and be able to interpret the results that derive from their solution.

Knowledge and understanding.
After attending the course the students know and understand the main probabilistic concepts (events, random variables, probability distributions)

Applying knowledge and understanding.
At the end of the course the students are able to formalize real problems and to solve them by applying the specific methods of the discipline.

Making judgements.
Students develop critical skills through the application of probabilistic theory.

Communication skills.
Students, through the study and performance of practical exercises, acquire the technical-scientific language of the discipline, which must be used appropriately in both the intermediate and final written tests and in the oral tests.

Learning skills.
Students who pass the exam have learned a method of analysis that allows them to tackle the subsequent teachings of statistical-probabilistic area.

Educational objectives

Learning Goals
The course tackles the subjects and problems of the classical Financial Mathematics and aims at providing theoretical notions and operational capacities that enable to solve the main financial problems in certainty conditions that arise in business and financial markets.

Knowledge and understanding
The student will learn, from a theoretical and operational point of view, the main financial schemes, tools for the assessment of income and for amortization schedules, the main criteria for financial decisions under certainty and, the tools to estimate the term structure of interest rates and financial immunization.

Applying knowledge and understanding
Each theoretical concept will be applied to real cases. Students will be assessed according to their ability to solve specific problems

Making Judgements
Each student will be required to download real market data and build the term structure of interest rates or a repayment of loan plan in order to be able to validate his/her ability to do so

Communication Sklls
Each student will be required to present the application of studied methodologies to solve a real problem

Learning Skills
The learned concepts will be tested having each student to undertake a final exam

Educational objectives

Learning goals.
The main learning goal for students is the knowledge of principles and methods of Statistical inference.
Students must be able to apply the main inferential techniques and to interpret the results of their use on real data.

Knowledge and understanding.
Students acquire knowledge and understanding of the most important inferential problems (point estimation, interval estimation, hypothesis testing) and of the main methods for solving these problems (maximum likelihood estimates, confidence intervals, parametric tests).

Applying knowledge and understanding.
After the attendance of this course, students will be able to formalize real problems into inferential problems and to apply appropriate inferential methods.
They will be able to use the main parametric models and to apply methods to models not considered in classwork.
They will also be able to apply inferential techniques ti real data and to interpret them.

Making judgements.
Students improve judgements skills by applying inferential methods to a wide range of statistical models.
Their skills will be improved by using and comparing different methods to the same problems and by applying these methods to real data.

Communication skills
Students will acquire the scientific language of Statistics, that will be used in written and oral tests.
Communication skills will be enhanced also by group work.

Learning skills.
Students will acquire the fundamental knowledge needed to study formal inferential properties of more complex models in more advanced classes.

Educational objectives

Learning goals
Working knowledge of the main models of economic dynamics

Knowledge and understanding
Upon succesfull completion of the course, students will be able to analyse actual economic problems in terms of competing theories and models.

Applying knowledge and understanding
Upon succesfull completion of the course, students will be able to understand the explicit and implicit hypotheses informing the main economic policy proposals in the current debate.

Making judgements
The course is explicitly based on the principle of methodological and theoretical pluralism. Students will be introduced to at least two competing models for each economic problem considered, and will understand the criteria with which to personally choose their favourite interpretation

Communication skills
Through study and hands-on sessions, students will become proficient in the jargon and technical language of the discipline, which they must use in both written and oral examinations.

Learning skills
Students that succesfully complete the course will have learnt a method of analysis that will allow them to tackle and understand the main economic issues of today, both in subsequent economic courses and in the fruition and participation to the public debate

Educational objectives

Learning goals.
The course is meant to expose students to a number of major topics in Economics of Risk and Ambiguity, linking theory with some empirical regularities.

Knowledge and understanding.
The course is supposed to broaden students' knowledge of the various theories, both classical and behavioural, their implication and the way these are empirically and/or experimentally verified.

Applying knowledge and understanding.
Upon successful completion of the course, students will be able to understand the main classic theories of choice under risk and ambiguity, the rationale behind the alternative theories, their implication and relevance in explaining the empirical regularities, which are not captured by standard approaches.

Making judgements.
The course develops in a way to spurs students on inferring theories from empirical evidence.
Such an approach is supposed to provide them with instruments to analyse critically situations, both theoretical and empirical, that involve judgement under risk and ambiguity.

Communication skills.
Through study and hands-on sessions, students will acquire the terminology characterising the discipline, which they are required to use in both written and oral examinations.

Learning skills.
Students who complete the course successfully will be acquainted with a method of analysis enabling them to tackle the main economic issues concerning judgment under risk and ambiguity, both in subsequent economic courses and in the fruition and participation to the public debate.

Educational objectives

Learning goals.
The main goal of the course is the acquisition of the fundamental statistical tools for the analysis of multivariate data and their use in real applications.
At the end of the course, the student should be able to formalize the statistical goal of a real case study, to develop a strategy of analysis by selecting appropriate methods, to apply the methodology and derive the correct conclusions by producing a (short) technical report which selects and collects the main the results.

Knowledge and understanding.
When completing the course, students will have learnt the main issues and essential concepts of multivariate and multidimensional analysis (for example, dependence, dimension reduction, classification) and the standard methodologies to face and handle such problems (such as, linear regression, PCA and cluster analysis).

Applying knowledge and understanding.
When completing the course, students will be able to formalize a multivariate statistical problem and select the appropriate methodologies to face such a problem.
Moreover, they will have the basic skills to explain possible choices, to make comparisons and to assess assumptions and applicability.
Finally, they will be able to apply the methods to real data and interpret the results.

Making judgements.
Students develop the critical thinking by applying the methodologies learnt which they will be able to use in autonomy by means of statistical software.
The capability to process data and produce the output by themselves reveals the autonomy in analyzing, making judgements necessary to make choices and comparisons taking into considerations theoretical criteria.
In addition, students will learn to critically interpret the results obtained in real applications.

Communication skills.
By processing data and making short technical reports, students will learn the correct use of the technical language which is required in both coursework and final exam.
Special attention is given to the skill of communicating results to non-specialists by using a rigorous but understandable language.

Learning skills
Students passing the exam have learnt:
a) the theoretical background in advanced statistics to possibly pass to a Second Cycle Degree in either Statistics or Applied Statistics;
b) the tools to develop and build a strategy of analysis in autonomy when analyzing data which are necessary either to tackle a job or to continue the Programme of Study.

Educational objectives

Learning goals aims and objectives
Critical understanding of capital market modeling, of pricing models and related financial problems; proficiency in the use of quantitative techniques and evaluation criteria for financial choices; ability to collect, interpret and select data characterising financial contracts and markets, knowledge of financial jargon and relevant linguistic correspondences (Italian-English).

Knowledge and understanding.
Base elements of Calculus, Probability, and Statistics.

Applying knowledge and understanding.
Ability to apply quantitative methods to portfolio selection, to the valuation of derivatives and financial contracts, to the analysis of financial markets; critical tools for reading and interpreting contracts and financial market conditions.

Making judgements
Critical tools for the evaluation of literature of the field.

Communication skills.
The studens will have to be able to talk - with knowledge and insights- on the problem of portfolio selection and on base elements of financial markets.

Learning skills.
The student will be able to apply mathematical and software tools to Portfolio selection problem and base financial markets.

Educational objectives

The main objective of the course is to provide students with the main tools to analyse time series in economics and finance, to make forecasts and to evaluate them.

Knowledge and understanding.

After attending the course, students will be able to describe, interpret and forecast economic time series, distinguishing seasonal, short-term, and long-term fluctuations.

Applying knowledge and understanding.

After attending the course, the students will know the main statistical tools to analyse temporal dependent data, and will be able to implement the analysis on real time series through statistical software.

Making judgements.

Students will increase not only their theoretical skills but also their critical curiosity in reading real recent economic phenomena.

Communication skills.

Students, through discussions in the classroom and exercises, will acquire tools for critical analysis of empirical evidence and communication skills.

Learning skills.

Students learn methods of analysis that will allow them to critically read an economic report.

Educational objectives

Learning goals:

The course aims at providing knowledge on financial markets, in order to illustrate, through different approaches, the importance of these markets for the determination of the real variables of the economy, such as consumption, income, investment, development and inequalities.

The financial balances of the economy and the national accounting principles will be analyzed in detail, such as: financial constraints on economic activity in conditions of certainty and uncertainty; diversification; asset allocation; portfolio optimization; behavioral finance. Further topics will include market efficiency, the efficiency and stability of the banking systems and the financial globalization and global financialization of modern society.

The course aims to understand the role of financial markets and the institutions operating in them, in particular banks.

a) Knowledge and understanding

The students who complete this course will learn to read the dependence between financial markets and the functioning of the real economy, developing theoretical and practical skills useful for a career or further studies in finance.

b) Applying knowledge and understanding

Thanks to a detailed overview of many aspects of the financial markets and the current financial globalization and the use of real examples, at the end of the course, the students will be able to formalize the real economic problems and to apply the methods specific to the discipline to solve them. Students will acquire theoretical preparation and, thanks to the analysis of numerous practical cases, the ability to critically study national and international financial markets and to evaluate efficient portfolio combinations in different contexts.

c) Making judgments

The students will increase not only their theoretical skills but also their critical curiosity in reading economic and financial phenomena and the global financialisation that characterizes the current economic context.

d) Communication skills

Students, through discussions, drawn from reading newspapers such as the Financial Times, and classroom exercises, will acquire tools for market analysis and financial tools and communication skills. They will also learn how to structure and present a research report.

e) Learning skills

The students who have passed the exam have learned methods of analysis that will allow them to face other economic courses.

Educational objectives

The final exams consists of writing, presenting and discussing a thesis, developed autonomously by the students, which illustrates in a coherent and detailed manner the problem tackled during the practical training and all the activities carried out to develop its solution.