B020934 - PORTFOLIO CHOICE AND OPTIMIZATION - MOD.A

English

(Module 1 - 6 CFU - Zezza) Important models in finance can be classified as linear. We describe the simplex allgorithm which can be used to solve them numerically, we will analyse in depth how the algorithm works, the problems which can arise while using it and its efficiency. he second part will deal with GAMS (General Algebraic Modeling System), a modeling language, which will be used to describe and solve some cases studies in finance

(Module 1 - 6 CFU - Zezza) Notes provided by the teacher
(Module 2 - 3 CFU - Livieri) Notes provided by the teacher

The general purpose is to make the student familiar with some numerical solution methods and to use a specific modelling language by analysiing a case study and preparing the required code.

(Module 1 - 6 CFU - Zezza) The math prerequisite for the course is a basic knowledge of Linear Algebra.
(Module 2 - 3 CFU - Livieri) The are basically no prerequisite for this part of the course.

Academic lessons and practical coding sessions

(Module 1 - 6 CFU - Zezza) Linear Programming: Three Homework (5%)
A short presentation of 15 minutes about a given topic (5%)
A Final written exam followed by a short discussion on it (40%)
GAMS.
Two Homework (10%)
A case study to examine autonomously, including data retrieval and coding (40%).

(Module 2 - 3 CFU - Livieri) Study and (a short) presentation of a research paper
on some of the topics presented in the course.

(Module 1 - 6 CFU - Zezza) This module will be divided into two parts, each weighting 3 CFU each. The general purpose is to make the student familiar with some numerical solution methods. To reach this goal, we will study a specific kind of model and a specific algorithm in the first part while in the second part we will describe a modelling language, available on line, which will be used to solve different kind of models with different kinds of algorithms.

PART 1

Linear Programming. By a case study in finance we will analyse Linear Models which are characterized by a linear objective function and by a set of linear equality and/or inequality constraints. We will introduce the Simplex algorithm which can be used to solve numerically these problems and we will analyse in depth how an algorithm works, the problems which can arise while using it and its efficiency.

PART 2.

GAMS. The General Algebraic Modelling System, is a modelling language which can be used to describe many different types of models (not only linear ones) and we will use it to describe financial models and to solve them by calling some other computer programs implementing the algorithms. The course requires some previous knowledge of Linear Algebra.

(Module 2 - 3 CFU - Livieri) This part of the course is mainly theoretical and it is devoted to a review and presentation of the standard portfolios theories. More precisely, We will start by describing the mechanism of the choices under risk and the criterion of expected utility theory. Then, We will move to the so-called mean-variance criterion introduced by Markowitz (1952) and to a comparison of the latter with the criterion of expected utility. In the third and fourth lecture We will give the definition of efficient portfolios and We will study (in-depth) the construction of the efficient frontier. Finally, We will move to analyse the Capital Asset Pricing Model (CAPM), the consumption CAPM (C-CAPM) and the Arbitrage Pricing Theory (APT).