MATHEMATICS FOR FINANCE
Prof. Stefano Patrì
Syllabus of the Course and reference books
1) Linear Algebra
1.1) Vector spaces and subspaces
1.2) Concept of dimension and basis of a vector space
1.3) Change of basis in a vector space and its effect on the components of a vector
1.4) Linear applications between two vector spaces
1.5) Association of a matrix to a linear application
1.6) Kernel and image of a linear application and their properties
1.7) Quadratic forms, concept of eigenvalue and eigenvector of an endomorphism
1.8) Diagonalization of an endomorphism and of a quadratic form
2) Optimization of functions of several variables
2.1) Level curves and elements of topology of the n-dimensional space
2.2) Polar coordinates, limits, continuous functions
2.3) Differential calculus: derivative along a direction, differentiable functions
2.4) Optimization of free and constrained functions
2.5) Optimization of functions subject to constraints given by curves, Lagrange’s multipliers
3) Ordinary differential equations
3.1) Linear equations of order n: homogeneous and non-homogeneous case
3.2) Linear equations of order greater than 1 with constant coefficients
3.3) Non linear equations of order 1: separation of the variables and Bernouilli equation
4) Application to Finance
4.1) Yield curve, spot and forward rates
4.2) Yield to maturity, cash flow valuation
PROGRAM AND DATE OF EVERY LESSON
Reference books
1) J. Bergin, Mathematics for Economists with Applications, Routledge, 2015 (downloadable HERE)
2) C. Byrne, A First Course in Optimization, CRC Press, 2015 (downloadable HERE)
3) S. Lang, Linear Algebra, Springer-Verlag, 3rd Ed., 1987 (downloadable HERE)
4) S. Lang, Introduction to Linear Algebra, Springer-Verlag, 2nd Ed., 1986 (downloadable HERE)
5) S. Lang, Algebra Lineare, Bollati Boringhieri, 1984 (in ITALIAN, downloadable HERE)
6) M. Rosser, P. Lis, Basic Mathematics for Economists, Routledge, 2016 (downloadable HERE)
7) C. P. Simon, L. Blume, Mathematics for Economists, Norton, 1994 (downloadable HERE)
8) C. P. Simon, L. Blume, Mathematics for Economists – Solutions to the Exercises, Norton (downloadable HERE)
9) R. K. Sundaram, A first Course in Optimization Theory, Cambridge University Press, 1996 (downloadable HERE)