# MODERN PORTFOLIO THEORY

iten
Code
41605
ACADEMIC YEAR
2020/2021
CREDITS
6 credits during the 1st year of 8700 Economics and Financial Institutions (LM-56) GENOVA
SCIENTIFIC DISCIPLINARY SECTOR
SECS-S/06
LANGUAGE
English
TEACHING LOCATION
GENOVA (Economics and Financial Institutions)
semester
2° Semester
Teaching materials

## OVERVIEW

 An introduction to mathematical methods of portfolio theory.

## AIMS AND CONTENT

LEARNING OUTCOMES

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.

AIMS AND LEARNING OUTCOMES

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.

PREREQUISITES

Basic mathematics.

TEACHING METHODS

Lessons held by the instructor

SYLLABUS/CONTENT

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. Brownian motion and Black-Scholes model

RECOMMENDED READING/BIBLIOGRAPHY

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.

## TEACHERS AND EXAM BOARD

Office hours: Office hours: Thursday h.15-17 &nbsp;

Exam Board

SALVATORE FEDERICO (President)

MARIA LAURA TORRENTE

## LESSONS

TEACHING METHODS

Lessons held by the instructor

LESSONS START

II semester

## EXAMS

EXAM DESCRIPTION

Written examination

ASSESSMENT METHODS

Written examination

Exam schedule

Date Time Location Type Notes
18/12/2020 10:00 GENOVA Orale
14/01/2021 13:00 GENOVA Orale
28/01/2021 13:00 GENOVA Orale
05/05/2021 10:00 GENOVA Scritto Appello straordinario riservato esclusivamente ai laureandi a.a. 2019/20
07/06/2021 10:00 GENOVA Scritto
21/06/2021 10:00 GENOVA Scritto
12/07/2021 10:00 GENOVA Scritto
06/09/2021 10:00 GENOVA Scritto

FURTHER INFORMATION

 Attendance Not mandatory.