Calculus, Linear Algebra, and basic Mathematics.

The student will be able to use the main mathematical instruments to study and solve optimization problems in economics and finance.

At the end of the course, the student:

• will be able to address particular problem arising in Mathematics of Finance
• will have available an important cultural baggage about Mathematical Analysis
• will have available powerful tools, both theoretical and about Computer Science, capable of addressing optimization problems with important Economic applications

• Financial flows: time value of money, annuities, present value and future value with simple and compounding rules, internal rate of return, spot and forward rate of interest, duration and price sensitivity.
• Matrices: eigenvalues, eigenvectors and quadratic forms.
• Functions of several variables: domain of functions, the gradient and its properties, the Hessian matrix, the Jacobian matrix, Taylor polynomials, unconstrained optimization, constrained optimization with equality constraints, constrained optimization with inequality constraints, economic and financial applications.
• Solving problems with Matlab

(A) C. P. Simon - L. E. Blume; Mathematics for Economists; W W Norton & Co Inc; London, 1994; Chapters: 7, 8, 9, 10, 12,13, 14.6, 16, 17, 18, 19, 23; ISBN: 978-0-393-11752-3

• The slant of the course is both theoretical and practical. In fact, each topic proposed comes with essential theory and application, with particular emphasis to the economical ones. Lectures can be either theoretical, exercise practice, and laborarories. Laboratories involve the use of the Matlab software.

  
  

  
  

• The exam is written and consists of a composition with open-ended questions.

  It takes place in a single phase and implies the resolution of multiple exercises based on the topics of the course. It is not possible to refer to books and texts during the exam. There is no midterm test. The adopted criteria consists in evaluating each exercise of the test. The evaluation takes mostly into account topic comprehension and then correctness of the calculations.

  
  

English.

English