TY - JOUR
T1 - Bayesian sequential testing for Lévy processes with diffusion and jump components
AU - Buonaguidi, B.
AU - Buonaguidi, Bruno
AU - Muliere, P.
PY - 2016
Y1 - 2016
N2 - 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.
AB - 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.
KW - Bayesian formulation
KW - Lévy processes
KW - Modeling and Simulation
KW - Statistics and Probability
KW - diffusion and jump components
KW - free-boundary problem
KW - optimal stopping
KW - sequential testing
KW - smooth fit principle
KW - Bayesian formulation
KW - Lévy processes
KW - Modeling and Simulation
KW - Statistics and Probability
KW - diffusion and jump components
KW - free-boundary problem
KW - optimal stopping
KW - sequential testing
KW - smooth fit principle
UR - http://hdl.handle.net/10807/133688
UR - http://www.tandf.co.uk/journals/titles/17442508.asp
U2 - 10.1080/17442508.2016.1197926
DO - 10.1080/17442508.2016.1197926
M3 - Article
SN - 1744-2508
VL - 88
SP - 1099
EP - 1113
JO - Stochastics
JF - Stochastics
ER -