Parametric Hawkes Processes: Theory, Simulation and Application

Abstract

In this Bachelor Thesis, an overview of Hawkes processes will be given. We start by looking at stochastic processes. We are particularly interested in the homogeneous and nonhomogeneous Poisson process, since these are the Markovian counterpart of Hawkes processes. Then Hawkes process will be defined. When familiar with the theory behind the Hawkes process, we spent time simulating these processes. Finally, we will be looking at applications of Hawkes processes, both in finance, and in the description of social media data.