Numerical methods for finance and portfolio optimization

The first part of the course (Portfolio Optimization) aims to introduce students to optimization methods for the construction of optimal portfolios. The identification of the optimal strategies will be presented under discrete time setup. In this context, specific methodologies will be discussed based on the nature of the assets in the portfolio.
The second part of the course (Numerical Methods for Finance) aims to provide a good knowledge of stochastic calculus and no arbitrage principles that constitute the foundations in the pricing of financial derivatives. The main numerical methods for pricing contingent claims will be presented during the course.

At the end of the course students will be able to use the main tools for pricing contingent claims and for constructing optimal portfolio strategies. They will possess a proper terminology and will acquire mathematical tools that allow to cope with numerical/financial problems that arise in financial institutions or in insurance companies. Finally they should be also able to produce scripts in the R programming language for financial analysis.