# MODERN PORTFOLIO THEORY

_
iten
Codice
41605
2020/2021
CFU
6 cfu al 1° anno di 8700 ECONOMIA E ISTITUZIONI FINANZIARIE (LM-56) GENOVA
SETTORE SCIENTIFICO DISCIPLINARE
SECS-S/06
LINGUA
Inglese
SEDE
GENOVA (ECONOMIA E ISTITUZIONI FINANZIARIE )
periodo
2° Semestre
materiale didattico

PRESENTAZIONE

An introduction to mathematical methods of portfolio theory.

## OBIETTIVI E CONTENUTI

OBIETTIVI FORMATIVI

The course aims at providing models and methods to theoretical and practical analysis of asset allocation problems. Special attention will be devoted to classical portfolio theory and empirical studies.

OBIETTIVI FORMATIVI (DETTAGLIO) E RISULTATI DI APPRENDIMENTO

Introduction to mathematical methods on arbitrage theory, option valuation, and portfolio allocation. The binomial model in the one period and multi-period case will be illustrated. In the one period case also more general models will be discussed. If time allows also the continuous-time Black-Scholes model will be introduced.

At the end of the course the student will be able to manage simple and implementable probabilistic models of financial markets.

PREREQUISITI

Basic mathematics.

Modalità didattiche

 Modalità didattiche Lessons held by the instructor Presente su Aulaweb Yes   X

PROGRAMMA/CONTENUTO

Part I. Basic discrete probability theory

Probability spaces. Random variables and distributions. Mean and variance.

Part II. The binomial financial model

1.  The One Period Model: Portfolios and Arbitrage; Contingent Claims; Risk Neutral Valuation.

2.  The Multiperiod Model: Portfolios and Arbitrage; Contingent Claims; Risk Neutral Valuation.

Part III. General (discrete probability) financial models

Absence of Arbitrage;  Martingale Measures; Martingale Pricing; Completeness; Stochastic Discount Factors

Part IV (if time allows). Brownian Motion and Black Scholes model

TESTI/BIBLIOGRAFIA

Bjork T., "Arbitrage theory in continuous time" (Third edition), Oxford University Press, 2009.

Shreve S., "Stochastic Calculus for Finance I: The Binomial Asset Pricing Model", Springer, 2004.

Chung K.L., "Elementary probability theory: with stochastic processes and an introduction to mathematical finance", Springer, 2006.

## DOCENTI E COMMISSIONI

Ricevimento: II semester: Wed h. 10.30-12.30

Commissione d'esame

SALVATORE FEDERICO (Presidente)

MARIA LAURA TORRENTE

## LEZIONI

Modalità didattiche

 Modalità didattiche Lessons held by the instructor Presente su Aulaweb Yes   X

INIZIO LEZIONI

II semester

## ESAMI

Modalità d'esame

Written examination.

Modalità di accertamento

 Modalità di accertamento Written examination. Ripetizione dell’esame Three times in the first session. It is mandatory to sign for the examination through the web portal.

Calendario appelli

Data Ora Luogo Tipologia Note
21/06/2021 10:00 GENOVA Scritto
12/07/2021 10:00 GENOVA Scritto
06/09/2021 10:00 GENOVA Scritto