Portfolio Optimization

A.Y. 2020/2021
Overall hours
Learning objectives
This course aims to introduce students to optimization methods for the construction of optimal portfolios.
The identification of the optimal strategies will be presented under two different setups. In the first investors are not allowed to rebalance the portfolio during the period of the investment and the optimal weights are fixed at the beginning of the time horizon by maximizing some measures of investor's satisfaction or by minimizing an appropriate risk measure. In this context specific methodologies will be discussed based on the nature of the assets considered in the portfolio.
In the second setup the possibility of rebalancing the structure of portfolio are introduced in discrete and continuous time framework.
Expected learning outcomes
At the end of the course students will be able to determine optimal portfolio strategies based on investor preferences. Students will become familiar with the construction of portfolios in a static and in a dynamic context, will possess a proper terminology and will acquire mathematical tools that allow to cope with portfolio optimization problems that arise in financial institutions or in insurance companies.
Course syllabus and organization

Single session

Lesson period
First trimester
All information will be posted on the course webpage on http://ariel.unimi.it.

Lectures will take place in presence. In case of a new directive from the University due to a
worsening of the situation, Lectures will take place online in synchronous way on the Zoom (or MSTeams) platform according to the timetable provided by the University. Lectures will possibly be recorded and made available to the students to be followed in an asynchronous way.

The program of the course will not change.

The written exams during the emergency will maintain the same structure of the usual ones.
Course syllabus
1 Asset-Liability Management
1.a Review of Bond Evaluation, Duration, Convexity
1.b Immunization Theory
- Fisher and Weil Theorem
- Redington Theorem
- Advances

2 Optimal Static Portfolio Selection
2.a Preferences Representation and Risk Aversion
2.b Stochastic Dominance
2.c Mathematics of Portfolio Frontier

3 Introduction of Optimal Dynamic Portfolio Selection
3.a Discrete-Time Framework
3.b Continuous-Time Framework
Prerequisites for admission
The students must have some preliminary knowledge of calculus,
standard financial mathematics, linear algebra, probability, integrals and optimization tchniques.
Teaching methods
Teaching Resources
Barucci E., Fontana C. "Financial Markets Theory: Equilibrium Efficiency and Information" Second Edition Springer (Chapters 2,3,6)

Bjork T. "Arbitrage Theory in Continuous Time" Third Edition Oxford Finance. (Chapters 4-5-6-19-20)

Cornuéjols G., Pena J., Tutuncu R. "Optimization Methods in Finance" Second Edition Cambrige University Press (Chapters 3,5,6,7,11,12,14)
Assessment methods and Criteria
Written exam composed of practical exercises and theoretical questions.
Through the theoretical questions, the students have to show that they
understood correctly the theory behind the construction of an optimal portfolio.
As practical exercises, students have to choose the best method
among those discussed in classes, apply them in a correct way.
Lessons: 40 hours
Professor: Mercuri Lorenzo
Educational website(s)
Tuesday from 2.30 p.m. to 5.30 p.m.
Microsoft office Teams (https://work.unimi.it/servizi/servizi_tec/1536.htm)