Discrete-Time Finite Horizon Approximation of Infinite Horizon Optimization Problems with Steady-State Invariance

Econometrica ◽  
1994 ◽  
Vol 62 (3) ◽  
pp. 635 ◽  
Author(s):  
Jean Mercenier ◽  
Philippe Michel
Keyword(s):  
Steady State ◽  
Discrete Time ◽  
Optimization Problems ◽  
Infinite Horizon ◽  
Finite Horizon ◽  
Infinite Horizon Optimization

NECESSARY AND SUFFICIENT CONDITIONS FOR DYNAMIC OPTIMIZATION

2014 ◽  
Vol 20 (3) ◽  
pp. 667-684 ◽  
Author(s):  
A. Kerem Coşar ◽  
Edward J. Green
Keyword(s):  
Optimization Problems ◽  
Infinite Horizon ◽  
Sufficient Conditions ◽  
Transversality Condition ◽  
Necessary And Sufficient Conditions ◽  
Infinite Horizon Optimization ◽  
Sufficient Conditions For Optimality ◽  
The Government ◽  
Duality Approach ◽  
Necessary And Sufficient

We characterize the necessary and sufficient conditions for optimality in discrete-time, infinite-horizon optimization problems with a state space of finite or infinite dimension. It is well known that the challenging task in this problem is to prove the necessity of the transversality condition. To do this, we follow a duality approach in an abstract linear space. Our proof resembles that of Kamihigashi (2003), but does not explicitly use results from real analysis. As an application, we formalize Sims's argument that the no-Ponzi constraint on the government budget follows from the necessity of the tranversality condition for optimal consumption.

scholarly journals Optimality criteria for deterministic discrete-time infinite horizon optimization

2005 ◽  
Vol 2005 (1) ◽  
pp. 57-80 ◽  
Author(s):  
Irwin E. Schochetman ◽  
Robert L. Smith
Keyword(s):  
Discrete Time ◽  
Efficient Solution ◽  
Optimality Criterion ◽  
Infinite Horizon ◽  
Optimality Criteria ◽  
Efficient Solutions ◽  
Regularity Conditions ◽  
Sufficient Condition ◽  
Infinite Horizon Optimization ◽  
Continuous State

We consider the problem of selecting an optimality criterion, when total costs diverge, in deterministic infinite horizon optimization over discrete time. Our formulation allows for both discrete and continuous state and action spaces, as well as time-varying, that is, nonstationary, data. The task is to choose a criterion that is neither too overselective, so thatnopolicy is optimal, nor too underselective, so thatmostpolicies are optimal. We contrast and compare the following optimality criteria: strong, overtaking, weakly overtaking, efficient, and average. However, our focus is on the optimality criterion of efficiency. (A solution isefficientif it is optimal to each of the states through which it passes.) Under mild regularity conditions, we show that efficient solutions always exist and thus are not overselective. As to underselectivity, we provide weak state reachability conditions which assure that every efficient solution is also average optimal, thus providing a sufficient condition for average optima to exist. Our main result concerns the case where the discounted per-period costs converge to zero, while the discounted total costs diverge to infinity. Under the assumption that we can reach from any feasible state any feasible sequence of states in bounded time, we show that every efficient solution is also overtaking, thus providing a sufficient condition for overtaking optima to exist.

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