This paper explores sufficient conditions for a continuous stationary Markov optimal policy and a concave valuefunction in stochastic dynamic programming problems. Also, the paper addresses conditions needed for the ...
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This paper explores sufficient conditions for a continuous stationary Markov optimal policy and a concave valuefunction in stochastic dynamic programming problems. Also, the paper addresses conditions needed for the differentiability of the valuefunction. The paper uses conditions such as first order stochastic dominance, second order stochastic dominance and concave stochastic dominance that are widely applied in economics.
The standard envelope theorems apply to choice sets with convex and topological structure, providing sufficient conditions for the valuefunction to be differentiable in a parameter and characterizing its derivative. ...
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The standard envelope theorems apply to choice sets with convex and topological structure, providing sufficient conditions for the valuefunction to be differentiable in a parameter and characterizing its derivative. This paper studies optimization with arbitrary choice sets and shows that the traditional envelope formula holds at any differentiability point of the valuefunction. We also provide conditions for the valuefunction to be, variously, absolutely continuous, left- and right-differentiable, or fully differentiable. These results are applied to mechanism design, convex programming, continuous optimization problems, saddle-point problems, problems with parameterized constraints, and optimal stopping problems.
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