Bayesian sequential testing for Lévy processes with diffusion and jump components

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.

Keywords:

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

AMS Subject Classifications:

• 60G40
• 62C10
• 62L10
• 35R35

Notes

No potential conflict of interest was reported by the authors.