Perov's Contraction Principle and Dynamic Programming with Stochastic Discounting

• Tác giả: Alexis Akira Toda
• Ngôn ngữ: eng
• Ký hiệu phân loại: 003.76 Stochastic systems
• Thông tin xuất bản: 2021
• Bộ sưu tập: Báo, Tạp chí
• ID: 166609

Tóm tắt

 This paper shows the usefulness of Perov's contraction principle, which generalizes Banach's contraction principle to a vector-valued metric, for studying dynamic programming problems in which the discount factor can be stochastic. The discounting condition $\beta<
 1$ is replaced by $\rho(B)<
 1$, where $B$ is an appropriate nonnegative matrix and $\rho$ denotes the spectral radius. Blackwell's sufficient condition is also generalized in this setting. Applications to asset pricing and optimal savings are discussed.