A Collocation Method for Sequential Testing Problems

A Collocation Method for Sequential Testing Problems

Abstract:

In this talk we illustrate a simple numerical method for the solution of a classical optimal stopping problem, namely sequential hypotheses testing. In particular, we discuss how the well known collocation method can be exploited in the Bayesian problem of sequential testing of two simple hypotheses about the features of a Lévy gamma process. This problem is appealing in applications because of the relevance of the gamma process in fields like risk theory and degradation and failure models.

In the first part of the presentation, we reduce the original optimal stopping problem to a free-boundary problem where the value function satisfies a linear integro-differential equation and the principles of the smooth and continuous fit. In the second part, we show how a collocation technique can be used to solve the free-boundary problem. The proposed numerical technique is also employed in well-understood problems to assess its efficiency.

Biography:

Bruno Buonaguidi is a Post-Doctoral Fellow at the InterDisciplinary Institute of Data Science at USI. His field of study is the theory of optimal stopping with applications to statistics and finance. He earned a Bachelor's degree in Economics (2007) and a Master's degree in Finance (2009) at the University of Pisa. He received his PhD in Statistics at Bocconi University (2014) with a dissertation on problems of sequential hypotheses testing and sequential change-point detection. He is currently the principle researcher in a project funded by the AXA Research Fund to develop early detection techniques for sudden changes occurring in certain classes of processes; the goal is to apply the results of this research to the efficient detection of frauds in credit card transactions. His work has been published in international journals of statistics, stochastic processes and sequential analysis

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