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14/12/2017, 16:00 — 17:00 — Abreu Faro Amphitheatre

Cláudia Nunes Philippart, *Instituto Superior Técnico, CEMAT - Universidade de Lisboa*

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Decide to Win

In the finance world there are many problems related with the optimal time to undertake some action. One of the most common problems is the derivation of the exercise time of an American option. But also in decisions regarding investments this question is essential. Questions like: when to adopt a new technology? When to invest in a new airport? When should suspension out of production occur? These problems have a real impact in the economy, and therefore one needs a proper mathematical formulation and solution for them.

In this talk we address such problems. They are known in the literature as optimal stopping problems, closely related with free boundary problems. One way to solve the optimisation problem is to use a variational inequality, known as the Hamilton-Jacobi-Bellman equation (HJB, for short). In the first part of the talk we present briefly the mathematical formulation and tools to solve such problems, and in the second part we show some applications, providing solution and discussion.