Mathematical methods for finance

A.A. 2017/2018
Insegnamento per
9
Crediti massimi
60
Ore totali
Lingua
Inglese
Obiettivi formativi
This course aims at introducing modern and advanced mathematical techniques for financial applications.

Struttura insegnamento e programma

Edizione attiva
Responsabile
Lezioni: 60 ore
Docente: La Torre Davide
STUDENTI FREQUENTANTI
Programma
Review of calculus for functions of one and several variables. Unconstrained optimization: first and second order optimality conditions. Convex optimization. Constrained optimization with equality constraints: The Lagrangian multipliers, optimality conditions. Constrained optimization with inequality constraints: KKT conditions.
Ordinary differential equations. Linear differential equations. Bernoulli and separable DEs. Systems of differential equations. The notion of equilibrium. Stability analysis.
Introduction to Partial Differential Equations. The Laplace equation. The heat and the wave equation. Fourier series and the method of separation of variables.
Calculus of Variations (CoV). The simplest CoV problem. The Euler equation. Sufficient conditions under convexity/concavity. Optimal control. The Hamiltonian function, optimality conditions. The case of finite and infinite horizon. The transversality conditions. Dynamic programming. The HJB equation.
Matlab. How to implement and solve optimization problems, differential equations, and control problems using MatLab.
Propedeuticità
Calculus I and II.
Prerequisiti e modalità di esame
Closed-book exam.
Metodi didattici
Lecture, tutorial, and lab.
Materiale didattico e bibliografia
[1] Knut Sydsaeter, Peter Hammond, Atle Seierstad, Arne Strom, Further Mathematics for Economic Analysis, Financial Times Prentice Hall, 2008 (chapters 1,2,3,5,6,7,8,9,10).
[2] William E. Boyce, Richard C. DiPrima, Elementary Differential Equations and Boundary Value Problems, Wiley, 2012 (chapters 1,2,3,4,10)
[3] Sandro Salsa, Annamaria Squellati, Dynamical Models and Optimal Control, EGEA, 2007 (chapters 1,2,4,6,7,9,10,11)
STUDENTI NON FREQUENTANTI
Programma
Review of calculus for functions of one and several variables. Unconstrained optimization: first and second order optimality conditions. Convex optimization. Constrained optimization with equality constraints: The Lagrangian multipliers, optimality conditions. Constrained optimization with inequality constraints: KKT conditions.
Ordinary differential equations. Linear differential equations. Bernoulli and separable DEs. Systems of differential equations. The notion of equilibrium. Stability analysis.
Introduction to Partial Differential Equations. The Laplace equation. The heat and the wave equation. Fourier series and the method of separation of variables.
Calculus of Variations (CoV). The simplest CoV problem. The Euler equation. Sufficient conditions under convexity/concavity. Optimal control. The Hamiltonian function, optimality conditions. The case of finite and infinite horizon. The transversality conditions. Dynamic programming. The HJB equation.
Matlab. How to implement and solve optimization problems, differential equations, and control problems using MatLab.
Prerequisiti e modalità di esame
Closed-book exam.
Materiale didattico e bibliografia
[1] Knut Sydsaeter, Peter Hammond, Atle Seierstad, Arne Strom, Further Mathematics for Economic Analysis, Financial Times Prentice Hall, 2008 (chapters 1,2,3,5,6,7,8,9,10).
[2] William E. Boyce, Richard C. DiPrima, Elementary Differential Equations and Boundary Value Problems, Wiley, 2012 (chapters 1,2,3,4,10)
[3] Sandro Salsa, Annamaria Squellati, Dynamical Models and Optimal Control, EGEA, 2007 (chapters 1,2,4,6,7,9,10,11)
Periodo
Primo trimestre
Periodo
Primo trimestre
Modalità di valutazione
Esame
Giudizio di valutazione
voto verbalizzato in trentesimi
Docente/i
Ricevimento:
In aspettativa. Il ricevimento e' sospeso.
Stanza 30, DEMM