# Università degli Studi di Napoli "Parthenope"  ## Teaching schedule

2018/2019
Belonging course:
Course of Master's Degree Programme on ECONOMIC, FINANCIAL AND INTERNATIONAL SCIENCES
Disciplinary sector:
MATHEMATICAL METHODS OF ECONOMY, FINANCE AND ACTUARIAL SCIENCES (SECS-S/06)
Language:
Italian
Credits:
6
Year of study:
2
Teachers:
Cycle:
Second semester
Hours of front activity:
48

Italian

### Course description

The aim of this course is to provide the general concepts about portfolio selection of bond and stock after the introduction of necessary mathematical tools.

### Prerequisites

Basic knowledge of mathematics and probabilities, in addition to a basic knowledge of portfolio theory.

### Syllabus

Part I: Elements of Mathematics and Probability theory
i) Recall of integration theory, Integration by parts and by substitution. – Definite and semi-definite quadratic forms. – Constrained Optimization: first order necessary conditions for max/min with equality/inequality constrains. Second order sufficient conditions (local and global).
ii) Recall of Probability theory: fundamental properties, Axiomatic approach, Conditional probability and indipendecy, Bayes formula, discrete and continuous random variables, Mean and variance, Joint distributions (18 hours of lessons)
Part I: Models of Portfolio Selection
The decision problem – sort operator and its properties – certainty equivalent – expected value operator and the Saint Petersburg paradox – the axiomatic framework of expected utility – representation theorem – measures of risk aversion – Jensen inequality – stochastic dominance.
Mean – variance approach with n securities: analytic resolution of the optimization problem – determination of Markowitz frontier – proof of the two funds theorem – the risk free bond and the capital market line – derivation of CAPM formula– market and equilibrium prices – CAPM e market prices – asset pricing theorem – risk neutral probability. (30 hours of lessons)

Part I: Elements of Mathematics and Probability theory
i) Recall of integration theory, Integration by parts and by substitution. – Definite and semi-definite quadratic forms. – Constrained Optimization: first order necessary conditions for max/min with equality/inequality constrains. Second order sufficient conditions (local and global).
ii) Recall of Probability theory: fundamental properties, Axiomatic approach, Conditional probability and indipendecy, Bayes formula, discrete and continuous random variables, Mean and variance, Joint distributions (18 hours of lessons)
Part I: Models of Portfolio Selection
The decision problem – sort operator and its properties – certainty equivalent – expected value operator and the Saint Petersburg paradox – the axiomatic framework of expected utility – representation theorem – measures of risk aversion – Jensen inequality – stochastic dominance.
Mean – variance approach with n securities: analytic resolution of the optimization problem – determination of Markowitz frontier – proof of the two funds theorem – the risk free bond and the capital market line – derivation of CAPM formula– market and equilibrium prices – CAPM e market prices – asset pricing theorem – risk neutral probability. (30 hours of lessons)

### Teaching Methods

The course includes lectures during which the themes of the program will be discussed together with applications and examples. The teaching material is also made available through the Moodle e-learning platform.

### Textbooks

- Castellani, De Felice, Moriconi (2005), Manuale di Finanza vol.II – Teoria del portafoglio e mercato azionario, Il Mulino (selection of chapters)
- Luenberger (2013), Investment Science. Oxford University Press Inc. (selection of chapters).
- Lecture notes by the teacher.

### Learning assessment

The test consists in the sustaining of a written and an oral test. The written test consists of exercises to verify that students are able to use the mathematical tools and apply them to selection of portfolios. The oral test aims to assess the depth of understanding of theoretical knowledge and students will also have to show that they are able to clearly explain the fundamental concepts learned during the course.