On Bounds for Dynamic Programs

An operator theoretical model is used to provide a general framework for establishing bounds in dynamic programming by extrapolation methods. A set of bounds is found for a specified solution V of an operator equation v = Uv with an isotone operator U, containing many known bounds as a special case by applying the general setting to standard models (e.g., to Markovian decision models). New bounds are suggested for a finite horizon Markov renewal decision model.