Portfolio optimization
A.A. 2018/2019
Obiettivi formativi
Aims and objectives: This course aims to introduce students to the fields of multiple criteria decision making and stochastic optimal control. These advanced mathematical techniques are then used to solve portfolio optimization and selection problems.
Risultati apprendimento attesi
Non definiti
Periodo: Primo trimestre
Modalità di valutazione: Esame
Giudizio di valutazione: voto verbalizzato in trentesimi
Corso singolo
Questo insegnamento non può essere seguito come corso singolo. Puoi trovare gli insegnamenti disponibili consultando il catalogo corsi singoli.
Programma e organizzazione didattica
Edizione unica
Responsabile
Periodo
Primo trimestre
STUDENTI FREQUENTANTI
Programma
Review of scalar optimization. Main concepts of multiple criteria analysis. Methodological approaches. Portfolio management. Asset screening and selection. The mean-variance framework. Alternative portfolio selection criteria.
Refresh of dynamic programming. Stochastic dynamic programming. The HJB equation. Verification theorem. Existence and uniqueness of the value function. How to solve it. Consumption and portfolio rules. Index bonds. Merton's model. Fisher's index bond model.
Refresh of dynamic programming. Stochastic dynamic programming. The HJB equation. Verification theorem. Existence and uniqueness of the value function. How to solve it. Consumption and portfolio rules. Index bonds. Merton's model. Fisher's index bond model.
Propedeuticità
Prerequisites for this course include a good knowledge of the advanced mathematical tools presented in the Mathematical Methods for Finance course. Before taking this course it is recommended to pass the exam of Mathematical Methods for Finance.
Prerequisiti
The exam will last for one hour. The exam consists of several exercises, it is written and closed-book. To pass the exam a student needs to achieve 18/30.
Attending students can earn extra points by solving the assignments and the project work.
Attending students can earn extra points by solving the assignments and the project work.
Metodi didattici
Face-to-face lectures, assignments, project work.
Materiale di riferimento
STUDENTI NON FREQUENTANTI
[1] Michael Doumpos, Constantin Zopounidis, Multicriteria Analysis in Finance, SpringerBriefs in Operations Research, 2014 (chapters 2,5)
[2] Fwu-Ranq Chang, Stochastic optimization in continuous time, Cambridge University Press, 2004 (chapters 4,5)
[2] Fwu-Ranq Chang, Stochastic optimization in continuous time, Cambridge University Press, 2004 (chapters 4,5)
Programma
Review of scalar optimization. Main concepts of multiple criteria analysis. Methodological approaches. Portfolio management. Asset screening and selection. The mean-variance framework. Alternative portfolio selection criteria.
Refresh of dynamic programming. Stochastic dynamic programming. The HJB equation. Verification theorem. Existence and uniqueness of the value function. How to solve it. Consumption and portfolio rules. Index bonds. Merton's model. Fisher's index bond model.
Refresh of dynamic programming. Stochastic dynamic programming. The HJB equation. Verification theorem. Existence and uniqueness of the value function. How to solve it. Consumption and portfolio rules. Index bonds. Merton's model. Fisher's index bond model.
Prerequisiti
The exam will last for one hour. The exam consists of several exercises, it is written and closed-book. To pass the exam a student needs to achieve 18/30.
Materiale di riferimento
[1] Michael Doumpos, Constantin Zopounidis, Multicriteria Analysis in Finance, SpringerBriefs in Operations Research, 2014 (chapters 2,5)
[2] Fwu-Ranq Chang, Stochastic optimization in continuous time, Cambridge University Press, 2004 (chapters 4,5)
[2] Fwu-Ranq Chang, Stochastic optimization in continuous time, Cambridge University Press, 2004 (chapters 4,5)
SECS-S/06 - METODI MATEMATICI DELL'ECONOMIA E DELLE SCIENZE ATTUARIALI E FINANZIARIE - CFU: 6
Lezioni: 40 ore
Docente:
La Torre Davide
Docente/i