FINANCIAL MATHEMATICS PROBLEMS FOR BUSINESS

The course presents some tools employed in predictive and prescriptive analysis for business and society applications, with a focus on time-series forecasting methods. Building upon the skills acquired in the first year of the Master, the course will expand the toolbox of methods which can be employed for forecast/prediction and for decision making. Both theoretical and practical aspects of the analysis methods are discussed.

Knowledge and understanding skills.
Attendance and active participation at lectures and, related activities, as well as individual study, allow the student to acquire the following educational targets:
- knowing and using concepts necessary to describe and understand statistical and forecasting instruments available to the firms;
- handling the statistical techniques and methods useful to formalize financial decisions.

Ability to apply knowledge and understanding.
Attendance and active participation at lectures and related activities, as well as individual study, allow the student to acquire the following skills:
- ability to use quantitative tools in modeling and evaluating time series linked to financial operations;
- ability to select the most appropriate technique for solving the concrete problem in hand;
- ability to analyze and discuss specific financial situations presented in the form of case studies.

Judgment skills, communication skills, learning skills.
At the end of the course, the student should be able to:
- formulate rational justifications and properly argue for the approach used to analyze time series linked to financial problems and the related quantitative forecasting models;
- understand relative strengths and weaknesses of different approaches;
- formulate, implement and communicate an adequate analysis and financial interpretation for the statistical models and techniques.

There is no formal pre-requisite, but the course will rely on some mathematical and statistical background. Standard topics covered in Mathematics and Computational Tools for Economics and Management degree programs, as well as in Statistics courses are taken as granted. Previous knowledge of probability concepts and statistical software is highly beneficial.
Moreover, attention is lying in learning ‘good practice’ applied with some exercises. In particular the computing language Excel and R will be employed.

This course covers several statistical forecasting methods, which can be applied to solve financial mathematical problems in business contexts. Topics include time series decomposition, moving averages, exponential smoothing and state space models, inventory management. In addition, simulation methods will be studied for implementing and integrating forecasting results in practice.

The course outline is structured as follows:

- Introduction to different type of data set and their visualization
- Time series decomposition and data analysis (moving averages; error, trends and seasonality)
- Forecasting methods (Exponential smoothing and state space models)
- Error distributions and simulations
- ARIMA Models and Decision Making

All the topics will be presented with the Excel software and with an introduction to the R software. The R package fpp3 for Principles and Practice of Forecasting will be used.

Slides and material will be made available on Moodle.

The course textbooks will be used is the following:

Rob J Hyndman and George Athanasopoulos, Forecasting: Principles and Practice (3rd ed).

The final evaluation is based on an oral exam.
The overall exam is divided into two parts: the first part involves a data analysis project, to be submitted according to the deadlines announced in class and available on the Moodle platform, which should be consulted regularly. The second part is the oral exam, focusing on the discussion of the project and the course content.

Fifteen in-person lessons will be held, starting from February 15th to March 8th, scheduled weekly according to the class timetable.

English

Students are required to register for the course on the moodle platform of the university (moodle.unive.it).

The final evaluation is based on an oral exam.
The overall exam is divided into two parts: the first part involves a data analysis project, to be submitted according to the deadlines announced in class and available on the Moodle platform, which should be consulted regularly. The second part is the oral exam, focusing on the discussion of the project and the course content.

oral