École Nationale Supérieure de
Techniques Avancées

Abstract

This project’s aim is to get the law of an Ornstein-Uhlenbeck process’ hitting time for a given threshold value. Four different methods were tested. The Monte Carlo method gives accurate results, but requires too much computing time. However the Adaptive Multilevel Splittling Method seems to work fine. The other two methods consist in getting an expression of the law of the hitting time. The first would then require to be able to correctly estimate a given integral. The second, just as the Monte Carlo method, gives accurate results, but requires too much computing time. In conclusion, the Adaptive Multilevel Splittling Method is the most promising.