The course aims to strengthen the knowledge of mathematics acquired in a three-year degree course and to develop quantitative tools for modelling, examine and solve financial and economic problems.
At the end of the course the student will be able to:
- Solve static optimization problems with constraints.
- Discuss and examine the computational complexity of some classic economic and financial optimization problems.
- Understand the concept of arbitrage and its application in fixed income markets and in stock markets.
- Discuss, modelling and solve some basic dynamic systems.
- Evaluate the stability and equilibrium solutions of some classic dynamic systems.
- Use spreadsheets to approximate numerical optimal solutions to static and dynamic financial and economic problems.
Basic knowledge of statistics, linear algebra and calculus
The course consists in traditional theoretical lectures and practical lab sessions (using classic spreadsheet in Microsoft Excel). Both traditional lectures and practical sessions aim at fostering participation and class discussion
The exam consists in two parts:
- Oral discussion about applied assignments and case studies (33% of the final grade).
- Final oral exam (67% of the final grade).
The course will discuss and present methods and techniques that are relevant for evaluating, modelling and solving financial and economic problems.
Specifically, the course will cover the following topics:
- Static optimization with and without constrains. Practical economic and financial examples: the decision problem under uncertainty conditions; aversion to risk and measures; optimal investors’ choices in the fixed income market and in the stock market. Equilibrium in financial markets: Capital Asset Pricing Model and Arbitrage Pricing Theory.
Practical examples with Microsoft Excel.
- The concept of arbitrage and risk neutral valuation. Fundamental theorem of asset pricing and introduction to dynamic problems. Practical examples with Microsoft Excel.
- Extension to dynamic analysis in a deterministic world. Introduction to systems of differential equations and of difference equations. Stability and equilibrium problems. Some classic economic examples. Introduction to dynamic optimization. Pontryagin principles. Deterministic vs stochastic analysis: the example of intertemporal portfolio selection problem. Practical examples with Microsoft Excel.
