Bayesian sequential testing for Lévy processes with diffusion and jump components

Bruno Buonaguidi, B. Buonaguidi, P. Muliere

Risultato della ricerca: Contributo in rivistaArticolo in rivista

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.
Lingua originaleEnglish
pagine (da-a)1099-1113
Numero di pagine15
RivistaStochastics
Volume88
DOI
Stato di pubblicazionePubblicato - 2016

Keywords

  • Bayesian formulation
  • Lévy processes
  • Modeling and Simulation
  • Statistics and Probability
  • diffusion and jump components
  • free-boundary problem
  • optimal stopping
  • sequential testing
  • smooth fit principle

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