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.
Buonaguidi, B., Muliere, P., Bayesian sequential testing for Lévy processes with diffusion and jump components, <<STOCHASTICS>>, 2016; 88 (7): 1099-1113. [doi:10.1080/17442508.2016.1197926] [http://hdl.handle.net/10807/133688]
Bayesian sequential testing for Lévy processes with diffusion and jump components
Buonaguidi, Bruno
Primo
;
2016
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.