Statistics, Finance and Actuarial sciences

Educational objectives

Learning goals.
The primary objective is to provide students with basic concepts and procedures of descriptive statistics.
At the end of the course the student must be able to design a small census survey and to conduct descriptive analyses of the data through the use of a statistical software.
Knowledge and understanding.
Upon completion of the course, students know and understand the main procedures of descriptive statistics.
They are able to organize data in simple and contingency tables and to synthesize them through graphical representations.
They know and are able to calculate the most important statistical indicators that measure
(a) position, variability and form of simple distributions and
(b) important aspects of the joint distribution of two variables.
Furthermore, they have acquired the notion of statistical model and are able to implement a simple regression model.
Applying knowledge and understanding.
Upon completion of the course, students are able to apply the knowledge acquired, in order to interpret and critically evaluate the results of descriptive analysis.
Making judgements.
Through a large number of exercises on all the topics covered, students develop autonomous judgment skills that allow to identify the most appropriate methods to solve problems of descriptive statistics and to critically interpret the results of the elaborations provided by the software.
Communication skills Students, through the study and the performance of practical exercises, acquire the technical-scientific language of the discipline, that must be properly used both in the written and in the oral examinations.
Learning skills Students who pass the exam will have knowledge of the fundamental notions for the descriptive analysis of data.
They will also be able to implement simple codes to organize data in tables and synthesize them through graphics and/or calculation of important indicators.
Therefore, they have acquired the basics to learn what will be proposed in the subsequent statistical courses.

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 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.
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

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.
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

1. General goals
The course aims to provide students with a deep understanding of monetary policies, financial system mechanisms, and their interactions between monetary and financial markets and the real economy. General educational objectives include:
• Acquiring a solid understanding of basic concepts in monetary economics, including the role of financial institutions and central banks.
• Critically analyzing monetary policies, their motivations, and implications for both economic activity and financial and monetary markets.
• Stimulating students' interest in global financial dynamics and their relationship with the real economy.
2. Knowledge and understanding
Students will learn to:
• Understand key concepts of monetary economics, such as inflation, interest rate determinants, and monetary policy.
• Interpret and analyze financial data and relevant economic indicators for monetary analysis.
• Evaluate the role of financial institutions and monetary policies in the economy.
3. Applying knowledge and understanding
Upon completion of the course, students will be able to:
• Apply theoretical models and statistical tools learned in previous exams in the context of monetary and financial analysis.
• Interpret and forecast the effects of monetary policies on economic variables such as employment and economic growth, as well as financial variables such as securities prices and interest rates.
• Use financial data and macroeconomic indicators to assess monetary and financial conditions.
4. Making judgements
Upon completion of the course, students will be able to:
• Critically evaluate existing monetary policies and their consequences on the economy.
• Develop informed and reasoned opinions on national and international monetary and financial issues.
• Integrate theoretical and empirical knowledge to form autonomous judgments on the effectiveness of monetary policies and their impact on income and wealth distribution.

5. Communication skills
Upon completion of the course, students will be able to:
• Communicate complex concepts related to monetary economics clearly and precisely, both verbally and in writing.
• Actively participate in class discussions and presentations on topics related to monetary economics.
• Understand and use the language and formal models of the discipline.
6. Learning skills
Upon completion of the course, students will be able to:
• Demonstrate autonomous learning skills by deepening their understanding of complex topics in the discipline.
• Understand the reasons and importance of pluralism in economics and the existence of alternative theories and schools of thought.
• Flexibly adapt to new theories and developments in the field of monetary and financial economics.

Educational objectives

This course can be chosen by the student within the Sapienza courses as long as consistent with the curriculum.

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.
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

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 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.