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.
The students must have some preliminary knowledge of calculus, standard financial mathematics, linear algebra, probability, integrals and optimization techniques.
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.