Mathematical methods for finance
A.A. 2018/2019
Obiettivi formativi
This course aims at introducing modern and advanced mathematical techniques for financial applications.
Risultati apprendimento attesi
Non definiti
Periodo: Primo trimestre
Modalità di valutazione: Esame
Giudizio di valutazione: voto verbalizzato in trentesimi
Corso singolo
Questo insegnamento non può essere seguito come corso singolo. Puoi trovare gli insegnamenti disponibili consultando il catalogo corsi singoli.
Programma e organizzazione didattica
Edizione unica
Responsabile
Periodo
Primo trimestre
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.
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
Prerequisites for this course include a good knowledge of the mathematical tools presented in Calculus I and II courses.
Prerequisiti
The exam will last for one hour. The exam consists of several exercises, it is written and closed-book. To pass the exam a student needs to achieve 18/30.
Attending students can earn extra points by solving the assignments and the project work.
Attending students can earn extra points by solving the assignments and the project work.
Metodi didattici
Face-to-face lectures, tutorials, lab.
Materiale di riferimento
STUDENTI NON FREQUENTANTI
[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)
[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)
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.
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
The exam will last for one hour. The exam consists of several exercises, it is written and closed-book. To pass the exam a student needs to achieve 18/30.
Materiale di riferimento
[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)
[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)
SECS-S/06 - METODI MATEMATICI DELL'ECONOMIA E DELLE SCIENZE ATTUARIALI E FINANZIARIE - CFU: 9
Lezioni: 60 ore
Docente:
La Torre Davide
Docente/i