Unbounded Markov Dynamic Programming with Weighted Supremum Norm Perov Contractions

• Tác giả: Alexis Akira Toda
• Ngôn ngữ: eng
• Ký hiệu phân loại: 005.116 +*Constraint programming
• Thông tin xuất bản: 2023
• Bộ sưu tập: Báo, Tạp chí
• ID: 198306

Tóm tắt

This paper shows the usefulness of the Perov contraction theorem, which is a generalization of the classical Banach contraction theorem, for solving Markov dynamic programming problems. When the reward function is unbounded, combining an appropriate weighted supremum norm with the Perov contraction theorem yields a unique fixed point of the Bellman operator under weaker conditions than existing approaches. An application to the optimal savings problem shows that the average growth rate condition derived from the spectral radius of a certain nonnegative matrix is sufficient and almost necessary for obtaining a solution.