---
title: "Final Project (Module A)"
subtitle: "Data Science for Insurance - a.y. 25- 26"
output:
  html_document:
    df_print: paged
  pdf_document: default
editor_options:
  chunk_output_type: console
---


```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

The data for the project can be obtained from any suitable source (e.g. Yahoo Finance, Kaggle, or R packages) and should consist of a d-dimensional dataset ($d\geq 3$) of risk factors or risk-factor changes. Examples include financial return series from a portfolio of assets or insurance loss data.
 
For instance, the following R packages contain financial and insurance datasets:

```
data(package = "copula")
data(package = "qrmdata")
data(package = "evir")

```
The analysis should include:

**(a)** *Marginal modelling*

Model each component separately. For financial return series, fit appropriate ARMA-GARCH models and validate them through residual diagnostics. For insurance loss data, select suitable parametric distributions capable of capturing skewness and heavy tails. The model choice should be justified.


**(b)** *Dependence modelling* 

Investigate the dependence structure by using copula functions. Specifically, the characterization of the dependence between the $d$ components can be addressed by

 - estimating association measures and/or tail dependence coefficients;
 
 - fitting one or more parametric copula models;
 
 - selecting the final copula model based on goodness-of-fit measures, graphical diagnostics, and/or statistical tests.


***Final Report***

Prepare a report of no more than 10 pages containing:

 - a description of the dataset and its main characteristics;
 - the code used for the analysis;
 - relevant tables, graphs, and model output;
 - model estimation and validation results;
 - comments on and interpretation of the findings.