Mathematical methods for finance

The aim of the course is to teach students the main techniques to approach multivariable optimization problems, both constrained and unconstrained, and to make students able to solve systems of differential equations and optimal control problems. The theoretical part of each module of the course will be enriched by a numerical part, where the goal is to get students acquainted with the main ideas and methodologies of numerical solutions with Matlab and Julia.

At the end of the course, students will be expected to possess and be able to use the main techniques for solving multivariable optimization problems, both constrained and unconstrained. Moreover, they will have the necessary backgrounds to categorize and, whenever possible, to solve analytically systems of differential equations and optimal control problems. Everywhere the analytical solution is out of reach, students will be equipped with the necessary numerical tools available in Matlab and Julia.