Abstract
We 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 minimizersf n at each stagen 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 we verify some analogous properties under stronger assumptions.
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Hinderer, K., Stieglitz, M. Increasing and Lipschitz continuous minimizers in one-dimensional linear-convex systems without constraints: The continuous and the discrete case. Mathematical Methods of Operations Research 44, 189–204 (1996). https://doi.org/10.1007/BF01194330
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DOI: https://doi.org/10.1007/BF01194330