Perov’s Contraction Principle and Dynamic Programming with Stochastic Discounting

When I was working on a series of papers on optimal savings and dynamic programming (Ma et al., 2020; Ma & Toda, 2021, 2022), I was not entirely happy with the proof technique because it relied on eventual contractions instead of contractions, and the argument was slightly complicated. One day in November 2020, I came up with an idea of generalizing the Banach contraction theorem to a matrix version using the spectral radius of a certain nonnegative matrix. I sent the paper to ORL, and after getting an R&R, I learned that the theorem I proved already existed as the Perov contraction theorem, so I rewrote the paper entirely to change the focus.