Abstract
Suboptimal solutions to infinite-horizon dynamic optimization problems with continuous state are considered. An underlying dynamical system determining the state transition between each stage and the next one is modelled via the constraints (xt, xt +1) ∈ D, t = 0, 1, …, where X is the set to which the state vector belongs and D ⊆ X × X is a correspondence. An error analysis is performed for two cases: approximation of the value function and approximation of the optimal policy function. Structural properties of the dynamic optimization problems are derived, allowing to restrict a priori the approximation to families of functions characterized by certain smoothness properties. The two approximation approaches are compared and the respective pros and cons are highlighted.
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