Mathematical Methods for Finance
A.Y. 2018/2019
Learning objectives
This course aims at introducing modern and advanced mathematical techniques for financial applications.
Expected learning outcomes
Undefined
Lesson period: First trimester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
First trimester
ATTENDING STUDENTS
Course syllabus
NON-ATTENDING STUDENTS
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.
Course 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.
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.
SECS-S/06 - MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES - University credits: 9
Lessons: 60 hours
Professor:
La Torre Davide
Professor(s)
Reception:
To schedule an online appointment, please reach out via email at [email protected]