This course addresses problems of optimal stopping, presenting one of the most used methodology: the so-called Hamilton-Jacobi-Bellman equations (HJB, for short). We focus, especially, in some financial applications like, for example, finance options and real options.
Optimal stopping problems are free-boundary problems, and thus one needs to invoke a verification theorem to prove that a solution of the HJB equation is also solution of the optimisation problem. We use the mathematics presented along the course to solve the problem of derivation of the optimal time for a firm to invest in a new project or market, in the sense that the firm maximizes its value.
Target audience: Master students with interest in financial applications and/or applications of differential equations and free boundary problems.
Course start date: 8th May, 2019
Course end date : 12th June, 2019
Applications start date: ongoing
Applications deadline: 22nd May, 2019
