Exponential Boundedness of Control Variables in a Sequentially Planned Bayesian Multiple Decision Problem in Continuous Time

Abstract

In this article we study the exponential boundedness properties of certain specifically structured control variables in a finite sequentially planned Bayesian multiple decision problem in continuous time investigated by Roters (Roters, M. A sequentially planned Bayesian multiple decision problem in continuous time. Sequential Anal. 2002, 21, 59–86.). More precisely, we prove that the total sampling time, the number of observation stages und the total sampling cost associated with these control variables possess a moment generating function in a neighborhood of the origin. All these appealing properties hold for the optimal control variable found in Roters (Roters, M. A sequentially planned Bayesian multiple decision problem in continuous time. Sequential Anal. 2002, 21, 59–86.).

Keywords:

• Bayes procedure
• Control variable
• Martingale
• Posterior distribution
• Termination properties
• AMS 1991 Subject Classification: Primary 62C10
• Secondary 60G40