The course consists of two parts: I) an introduction to financial mathematics (approximately 75% of the course); II) in-depth study of mathematics for economics (approximately 25% of the course). The objective of the first part is to provide basic skills and an overview of more advanced topics related to financial calculus using a problem-solving approach, and to develop the skills needed to implement the identified solutions on spreadsheets. At the end of the course, students will be able to: (a) solve financial valuation problems under certainty; (b) create spreadsheets that implement these solutions; (c) recognize some hedging and optimization problems for financial decisions. The objective of the second part is to introduce mathematical topics useful for economic analysis and of a more advanced nature than those covered in the Calculus course.
Course Prerequisites
Basic calculus and linear algebra.
Teaching Methods
Classroom lectures with slides and Excel spreadsheets.
Assessment Methods
Final written exam. Knowledge of the topics covered in the course will be verified, through applications and exercises. A scientific calculator is required for the test.
Texts
L. Barzanti, A. Pezzi; Matematica Finanziaria - Manuale operativo con Applicazioni in Excel, Seconda Edizione; Esculapio, 2014. L. Barzanti, A. Pezzi; Problemi Risolti di Matematica Finanziaria - Esercizi e Casi di Studio; Esculapio, 2014. Knut Sydsæter, Peter Hammond, Arne Strøm, Metodi matematici per l’analisi economica e finanziaria, a cura di Davide La Torre, Pearson Italia, Edizione 2021
Contents
The first part of the course is problem-solving-based, drawing on concrete financial problems to implement the necessary mathematical modeling. Both classical and spreadsheet-based modeling methods are developed. The topics covered are: 1. Simple operations, bonds. 2. Capitalization regimes; interest rates; the term structure of interest rates. 3. Composite operations: annuities; inverse problems; amortization. 4. Duration and financial immunization. 5. Investment choices. The second part will cover: 1. Complex numbers, eigenvalues and eigenvectors, diagonalization of square matrices, quadratic forms. 2. Multivariate calculus: gradients, directional derivatives, geometric representation, optimization in several variables. 3. Constrained optimization: Lagrange multiplier method; inequality constraints and Kuhn-Tucker conditions.
