Mathematical Finance

Credits

Prerequisites

None.

Scientific-disciplinary sector (SSD)

SECS-S/06 Mathematical Methods for Economics and Actuarial and Financial Sciences.

Examination method

Oral exam.

Learning
objectives

The course aims to provide advanced knowledge of mathematical models for financial decisions under uncertainty, with particular reference to stock markets, and to develop methodologies for portfolio selection, for modelling expectations and risk in markets, and for the structure and valuation of derivative contracts.

Syllabus

Elements of utility theory – Utility theory and portfolio selection – Mean-variance analysis of stock portfolios – The Capital Asset Pricing Model: identification of the equilibrium price of securities, risk decomposition – Arbitrage Pricing Theory – Options: combinations, the binomial option pricing model, the Black-Scholes model – Value at Risk (VaR).

Expected learning
outcomes

At the end of the course students must demonstrate that they

know and understand the issues involved in describing a financial problem by means of mathematical models, with particular regard to those characterised by uncertainty;
are able to apply the knowledge acquired by independently setting up a financial problem through modelling, and to solve the resulting model using appropriate mathematical methods;
are able to communicate ideas and solutions clearly, rigorously and effectively to both specialist and non-specialist audiences;
are able to identify the most appropriate methods to analyse and solve a problem related to the course topics and to interpret the results correctly.

Learning outcomes
to be assessed

Problem-solving skills; ability to model and interpret financial phenomena; command of the mathematical tools used in the course.

Mathematical Finance