Increasing and Lipschitz continuous minimizers in one-dimensional linear-convex systems without constraints: The continuous and the discrete case

The authors consider a stochastic control model with linear transition law and arbitrary convex cost functions, a far-reaching generalization of the familiar linear quadratic model. Firstly conditions are given under which the continuous state version has minimizers fn at each stage n which are increasing and in addition either right continuous or continuous or Lipschitz continuous with explicitly given Lipschitz constant. For the computationally important discrete version the authors verify some analogous properties under stronger assumptions.