Bayesian sequential testing for Lévy processes with diffusion and jump components. Issue 7 (2nd October 2016)

• Record Type: Journal Article
• Authors: Buonaguidi, B.; Muliere, P.
• Is Part Of: Stochastics. Volume 88:Issue 7(2016)
• Page Start: 1099
• Page End: 1113
• Publication Date: 2016-10-02
• Subjects: Bayesian formulation -- diffusion and jump components -- free-boundary problem -- Lévy processes -- optimal stopping -- sequential testing -- smooth fit principle; 60G40 -- 62C10 -- 62L10 -- 35R35; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/17442508.2016.1197926
• Languages: English
• ISSNs: 1744-2508

Abstract

Abstract : We study the Bayesian problem of sequential testing of two simple hypotheses about the Lévy-Khintchine triplet of a Lévy process, having diffusion component, represented by a Brownian motion with drift, and jump component of finite variation. The method of proof consists of reducing the original optimal stopping problem to a free-boundary problem. We show it is characterized by a second order integro-differential equation, that the unknown value function solves on the continuation region, and by the smooth fit principle, which holds at the unknown boundary points. Several examples are presented.