MATHEMATICS FOR ECONOMICS AND FINANCE
Prerequisites: Mathematics
The exam is written and consists of exercises both computational and theoretical. It can be taken in two modes.
1. General exam. During exam sessions, a two hours test on the whole program will be organized. The test scores up to 33 points and the exam is passed by achieving at least 18 points. Total score of more than 30 entails honor mark.
2. Two partial exams. During partial exams sessions a one hour exam on the part of the course just covered will be organized. The first partial test will propose questions primarily on financial calculation arguments and scores up to 33 points. The test is passed by achieving at least 15 points. The second partial test will propose questions mainly of probability calculations and scores up to 33 points. The test is passed by achieving at least 15 points. The examination is passed if the average grade of the two partial tests, rounded up, is greater than or equal to 18. Averages above 30 will entitle honor mark. Students who do not pass a partial test or get an average of less 18 will have to take the general exam.
At the end of the course students should be able to:
a) Construct common financial contracts, such as leasing contracts, consumer credit and loans;
b) Compute some legal indicators linked to financial contracts, such as TAN, APR, ISC;
c) Evaluate the convenience of some financial transactions according to the most accredited criteria that allow the maximization of profit in a given time horizon;
d) Critically comment on criteria inconsistent with the goal of maximizing profit as set time horizon;
e) Compute prices and yields of main fixed income securities, as well as the Duration and the underlying term structure;
f) Apply basic probability to managerial and financial problems.
The course will be held with lectures in which we will discuss the theoretical arguments and the methods of solution of the exercises. During classes, exercises will be proposed both for self assessment and class work.
Main topics cover:
• Capitalization and discounting: financial laws, financial laws in one and two variables.
• Standard Financial Contracts: depreciation, leasing and installment plans.
• legal indicators: TAN, APR, ISC.
• Financial valuations of non random investments.
• Term structure of interest rates and fixed-income securities.
• Financial immunization.
• Probability: different approaches to the definition and study.
• random experiments, events, probability, Bayes' Theorem.
• random variables: probability distribution and their moments.
• Expected value and variance of a linear transformation (affine) of a random vector.
Attendance is not mandatory, though highly recommended. Nevertheless, it is compulsory to study course material through textbook. The adopted texts are:
1. E. CASTAGNOLI, L. PECCATI, Matematica in azienda 1 (Calcolo finanziario con applicazioni), Milano, Egea, 2010.
2. E. CASTAGNOLI, M. CIGOLA, L. PECCATI, Probability. A Brief Introduction, Milano, Egea, 2009.
Lectures.