Mathematical Methods for Finance

A.Y. 2018/2019
Lesson for
9
Max ECTS
60
Overall hours
SSD
SECS-S/06
Language
English
Learning objectives
This course aims at introducing modern and advanced mathematical techniques for financial applications.

Course structure and Syllabus

Active edition
Yes
Responsible
SECS-S/06 - MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES - University credits: 9
Lessons: 60 hours
Professor: La Torre Davide
ATTENDING STUDENTS
Syllabus
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.
NON-ATTENDING STUDENTS
Syllabus
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.
Lesson period
First trimester
Lesson period
First trimester
Assessment methods
Esame
Assessment result
voto verbalizzato in trentesimi
Professor(s)
Reception:
On leave. Office hours are suspended.
Room 30, DEMM