Finance and insurance

VALERIA BIGNOZZI

The course introduces students to the foundations of statistical inference and the main methodologies of data science, with a specific focus on economic and financial applications. It presents the principal statistical models and techniques for regression, classification, clustering, and dimensionality reduction. By the end of the course, students will be familiar with the main statistical models and methods used for analysis in the economic, financial, and insurance domains. They will be able to identify the most appropriate methodologies for each problem and use statistical software for computation and data analysis to implement them. Students will apply statistical inference methods to real data for empirical analysis, correctly interpret model results, and assess their validity within the study context. They will develop autonomy in selecting the most suitable models for different analyses, justifying their choices based on complexity, interpretability, and predictive performance. They will be able to communicate results effectively through clear and coherent reports, integrating both code and analytical outputs. Finally, they will acquire an autonomous study method and the tools to deepen their understanding of new, including advanced, statistical methodologies, with the ability to implement them in a programming language.

1) Knowledge and Understanding
Upon completion of the course, students will be able to demonstrate a solid and comprehensive understanding of the statistical methods used in data science, with particular focus on applications in economics, finance, and actuarial science.
They will develop a critical awareness of both theoretical foundations (statistical inference, model selection, regularization) and practical methodologies (regression, classification, clustering, dimensionality reduction).
Students will also understand the methodological implications, strengths, and limitations of different techniques, and identify the contexts in which each method is most effective.

2) Applying Knowledge and Understanding
Students will be able to apply advanced statistical methods to real-world data, particularly in economic and financial settings, through hands-on exercises and individual projects.
They will competently use R software to conduct statistical analyses, interpret quantitative outputs, and make informed, data-driven decisions using both interpretable and “black-box” models.
They will work with techniques such as linear and nonlinear regression, model selection, regularization (LASSO, Ridge), supervised classification, clustering, and tree-based methods.
Students will also learn to translate statistical analyses into complete, concise, and well-structured written reports.

3) Making Judgements
Students will be able to critically assess the adequacy and robustness of statistical methods and models.
They will compare alternative modeling techniques, identify methodological limitations, and justify their methodological choices according to analytical goals and data characteristics.
They will also learn to manage trade-offs between model complexity and predictive accuracy, taking into account the validity of underlying assumptions.

4) Communication Skills
Students will develop the ability to communicate technical results effectively using appropriate statistical language and tools such as R Markdown, integrating code, output, and interpretation.
They will strengthen their ability to present methodological choices, interpret results, and discuss their implications clearly and professionally.
Through laboratory activities and individual or group projects, students will practice oral presentations and technical discussions on the topics covered in the course.

5) Learning Skills
Students will acquire the ability to work autonomously with R for advanced statistical analysis, even in unfamiliar situations not explicitly addressed in class.
They will be encouraged to pursue independent learning by exploring the literature and online resources.
The course provides a foundation for further study at the postgraduate level (Master’s or PhD) and for professional careers requiring continuous development of statistical and data analysis skills.

The course requires elementary knowledge of Descriptive Statistics, Inferential Statistics, and Probability. A basic understanding of Mathematics, including function analysis and matrix algebra, is also recommended. The course includes a programming component in R; therefore, familiarity with at least one programming language is advantageous, though not mandatory.

1. Basic of Statistical Inference (likelihood, testing, confidence intervals, likelihood function, estimators)
2. Overview of statistical learning
3. Linear regression
4. Classification and Clustering
5. Linear model selection and regularization
6. Moving beyond linearity
7. Tree-based methods
8. Applications to Financial and Actuarial Data using the R Programming Language

All the information about the course will be available at the following link:

https://elearning.uniroma1.it/course/view.php?id=20815

-Slides provided by the lecturer;

-An Introduction to Statistical Learning: with Applications in R (Springer Texts in Statistics) 2nd Edition 2021
by Gareth James (Author), Daniela Witten (Author), Trevor Hastie (Author), available on line at
https://www.statlearning.com/

-An Introduction to Statistical Learning: with Applications in R, 2nd Edition 2021
by Gareth James (Author), Daniela Witten (Author), Trevor Hastie (Author), disponibile on line al link
https://www.statlearning.com/

-Hastie, Trevor, Robert Tibshirani, and Jerome Friedman. "The elements of statistical learning." (2009).

-AI Tools for Actuaries

Classes will be held in person. For each statistical technique covered, there is a lecture-based component in which the instructor presents the theoretical aspects, application contexts, and limitations of the method, followed by an interactive component in which the methodologies are applied to real data from financial and/or actuarial contexts and discussed jointly by the instructor and the students. Part of the course also involves the use of the R programming language.

Attendance is not mandatory but strongly recommended.

The final assessment consists of two components with different weights:
a. 40% of the final grade will be based on the discussion of a report on a specific topic. This component assesses students’ ability to independently conduct advanced data analyses, prepare clear and well-structured reports, and present their findings to peers.
b. 60% of the final grade will come from an oral examination. This part aims to evaluate students’ theoretical knowledge, the depth of their understanding, and their ability to draw appropriate conclusions from the use of advanced statistical methods.

The exam consists of two parts: the discussion of a report (40% of the final grade) and an oral exam (60%).

In the first part, the instructor will provide students with a dataset to be analyzed using R. Students are then required to write a report, which will subsequently be discussed in class.
For example, students will be asked to:

1.a Describe the statistical technique chosen for the analysis (e.g., multiple linear regression, Poisson regression, or PCA), specifying:

the objectives of the model or technique,

the functional form or main procedure,

the fundamental assumptions regarding the observations and variables.

1.b Apply the technique to the dataset in R, showing:

how to estimate the parameters or calculate the principal components,

interpretation of the results (coefficient of determination, parameter significance, explained variance, etc.),

any numerical issues or critical points encountered (collinearity, outliers, missing data).

1.c Evaluate the quality and adequacy of the model or technique chosen, considering:

goodness-of-fit or variance-explaining criteria (R², deviance, AIC, percentage of variance explained),

validation tools (cross-validation, resampling, confusion matrix for predictive models),

limitations of the model or technique in relation to the application context, and possible extensions or alternative models.

GRADING:

1.a corresponds to Level 1 of Bloom’s taxonomy (“Remember”); correctly answering this sub-question contributes to achieving a passing grade (18/30).

1.b corresponds to Levels 2/3 of Bloom’s taxonomy (“Understand / Apply”); correctly answering this sub-question contributes to an intermediate grade (up to 26/30).

1.c corresponds to Levels 4/5 of Bloom’s taxonomy (“Analyze / Evaluate”); answering this sub-question fully and critically contributes to the maximum grade (30/30 with honors).

The second part of the exam consists of an oral test. The questions are aimed at assessing the student’s ability to identify the most appropriate statistical techniques for a given context and to discuss their application, properties, and limitations. For example, a question could focus on logistic regression:

QUESTION:
1.a Describe the binary logistic regression model, specifying:

the functional form of the model,

the role of the logit link function,

the main assumptions regarding the error term and the observations.

1.b Derive the likelihood function of the logistic regression model and explain the procedure for estimating the parameters using maximum likelihood. Explain why a closed-form solution is not possible and describe the role of iterative algorithms (e.g., Newton-Raphson or IRLS).
Show how the model is estimated in R using the glm() function.

1.c Discuss how to evaluate the quality of the logistic regression model, considering:

goodness-of-fit criteria (AIC, deviance),

predictive performance measures (confusion matrix, ROC curve, AUC),

issues in interpretation and model validity (multicollinearity, complete separation, overfitting).
Justify methodological choices based on the application context.

GRADING:

1.a corresponds to Level 1 of Bloom’s taxonomy (“Remember”); correctly answering this sub-question contributes to a passing grade (18/30).

1.b corresponds to Levels 2/3 of Bloom’s taxonomy (“Understand / Apply”); correctly answering this sub-question contributes to an intermediate grade (up to 26/30).

1.c corresponds to Levels 4/5 of Bloom’s taxonomy (“Analyze / Evaluate”); answering this sub-question fully and critically contributes to the maximum grade (30/30 with honors).

Additional information about the exam is available at the following link:
https://elearning.uniroma1.it/course/view.php?id=20815

• Review of Statistical Inference, 3 classes
  • Books: Slides


• General Concepts: Statistical Learning and Linear Regression, 3 classes
  • Books: Slides and  Chapters 2–3 of the textbook


• Classification, 2 classes
  • Books: Slides and  Chapter 4 of the textbook


• Resampling methods (cross validation and bootstrap), 2 classes
  • Books: Slides and  Chapter 5 of the textbook


• Linear Model Selection and regularization,  2 classes
  • Books: Slides and  Chapter 6 of the textbook


• Moving beyond linearity,  2 classes
  • Books: Slides and  Chapter 7 of the textbook


• Tree-based Methods,  2 classes
  • Books: Slides and  Chapter 8 of the textbook


• Practical exercises using R,  8 classes