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Rationalizing Policy Functions by Dynamic Optimization
Author(s) -
Mitra Tapan,
Sorger Gerhard
Publication year - 1999
Publication title -
econometrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 16.7
H-Index - 199
eISSN - 1468-0262
pISSN - 0012-9682
DOI - 10.1111/1468-0262.00023
Subject(s) - monotonic function , bellman equation , maximization , mathematical optimization , function (biology) , lipschitz continuity , mathematics , value (mathematics) , regular polygon , convex function , concave function , convex optimization , mathematical economics , pure mathematics , mathematical analysis , statistics , geometry , evolutionary biology , biology
We derive necessary and sufficient conditions for a pair of functions to be the optimal policy function and the optimal value function of a dynamic maximization problem with convex constraints and concave objective functional. It is shown that every Lipschitz continuous function can be the solution of such a problem. If the maintained assumptions include free disposal and monotonicity, then we obtain a complete characterization of all optimal policy and optimal value functions. This is the case, e.g., in the standard aggregative optimal growth model.