Infinite Horizon Dynamic Optimization With Unbounded Returns: Necessity, Sufficiency, Existence, Uniqueness, Convergence and a Sequence of Counterexamples

23 Pages Posted: 20 Dec 2018

See all articles by Agnieszka Wiszniewska-Matyszkiel

Agnieszka Wiszniewska-Matyszkiel

University of Warsaw - Institute of Applied Mathematics

Rajani Singh

University of Warsaw - Institute of Applied Mathematics

Date Written: December 3, 2018

Abstract

In this paper, we state sufficiency, necessity, convergence, existence and uniqueness results for infinite horizon optimal control problems with unbounded payoffs in which the assumptions are very weak and there are no topological assumptions about the model components. We also state a sequence of simple counterexamples for various popular false beliefs, often used over-simplifications of methodology or same incorrect results in this field.

Keywords: Dynamic Optimization, Infinite Horizon, Unbounded Payoffs, Feedback, Bellman Equation, Terminal Condition, Sufficiency, Necessity, Existence, Uniqueness, Convergence, Counterexample, Dynamic Games

JEL Classification: C02, C60, C61, Q20, Q30, Q50

Suggested Citation

Wiszniewska-Matyszkiel, Agnieszka and Singh, Rajani, Infinite Horizon Dynamic Optimization With Unbounded Returns: Necessity, Sufficiency, Existence, Uniqueness, Convergence and a Sequence of Counterexamples (December 3, 2018). Available at SSRN: https://ssrn.com/abstract=3295058 or http://dx.doi.org/10.2139/ssrn.3295058

Agnieszka Wiszniewska-Matyszkiel (Contact Author)

University of Warsaw - Institute of Applied Mathematics ( email )

ul Banacha 2
Warsaw, 02-097
Poland
+48 22 5544 486 (Phone)
+48 22 55 44 300 (Fax)

Rajani Singh

University of Warsaw - Institute of Applied Mathematics ( email )

Poland

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