•GUIDA ECONOMIA 07-08 - Università degli studi di Udine

prospectus udine
223
The Kuhn-Tucker multipliers theorem.
First order necessary conditions with
mixed constraints. Non-negative variables.
The modified Lagrangian and first
order necessary Kuhn-Tucker conditions.
Second order sufficient conditions.
- The envelope theorems.
Optimal solution and value function. The
envelope theorem. Conditions for the
local existence of a solution to the parametric
optimisation problem.
- The envelope theorems.
- Convex and concave functions. Quasiconcave
functions and pseudo-concave
functions.
Geometric and algebraic characterization
of concave and convex functions. Cobb-
Douglas functions. Quasi-concave and
quasi-convex functions. Pseudo-concavity
in a point and in a set. Sufficient conditions
for pseudo-concavity in a point.
- Concave programming.
Sufficient conditions for the maximum of
a class C 1 concave function. Optimization
for quasi-concave functions. Sufficient
conditions for the qualification of constraints.
Optimization for pseudo-concave
functions with quasi-convex constraints.
Bibliography
- SIMON-BLUME, Matematica 2 per l’Economia
e le Scienze Sociali, Univ. Bocconi Editore.
MATHEMATICS FOR ECONOMICS
Prof. Marcellino Gaudenzi
Contents
The space of n-dimensional real vectors.
Linear dependence and independence.
Subspaces. Bases. Dimension. Inner
product. Matrices. Matrix multiplication.
The determinant. Laplace and Binet theorems.
Inverse of a matrix. Rank of a
matrix. The Kronecker rule. Linear systems.
The Rouchè-Capelli Theorem.
Cramer’s Theorem. Linear functions.
Eigenvectors and eigenvalues of a matrix.
Similar matrices. Diagonalizable matrices.
The Cayley-Hamilton Theorem. Quadratic
forms (outlines).
Bibliography
- E. CASTAGNOLI, L. PECCATI, La matematica
in azienda; strumenti e modelli, Egea,
1996.
- M. D’AMICO, F. MARELLI, Matematica per
le applicazioni aziendali, I, Algebra lineare,
Etas Libri, 1996.
Exam
There will be a written examination consisting
of exercises and theoretical questions.
MATHEMATICS FOR FINANCE
(CdL BE, SCSBM)
Prof. Antonino Zanette
(CdL BF, EBA)
Prof.ssa Patrizia Stucchi
Contents
First Part. Mathematics of finance fundamentals
under certainty conditions. Elementary
financial transactions. Basic definitions:
interest, discount, final value,
present value, rates, factors. Financial
laws: homogeneity, uniformity, decomposability.
Financial rules: simple interest,
compound interest, simple discount.
Real rate of interest, nominal rate of
interest, force of interest, capitalization
factor and discount factor. Equivalent
rates. Spot and forward rates. The term
structure of interest rates.
Second Part. Taxonomy of annuities. Present
and future value of various types of
annuities (immediate-deferred, ordinarydue,
perpetuities, annuities payable k-
thly).
Loan amortization. Amortization sched-