Differentiability of the value function in continuous-time economic models

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:394

Article

Pablo Rincon-Zapatero, Juan¹  Santos, Manuel S.² 

[1] Univ Carlos III Madrid, Dept Econ, E-28903 Getafe, Spain

[2] Univ Miami, Dept Econ, Coral Gables, FL 33124 USA

关键词: Constrained optimization;    Value function;    Differentiability;    Envelope theorem;    Duality theory;   

DOI  :  10.1016/j.jmaa.2012.04.056

来源: Elsevier

【 摘 要 】

In this paper we provide some sufficient conditions for the differentiability of the value function in a class of infinite-horizon continuous-time models of convex optimization arising in economics. We dispense with the assumption of interior optimal paths. This assumption is quite unnatural in constrained optimization, and is usually hard to check in applications. The differentiability of the value function is used to prove Bellman's equation as well as the existence and continuity of the optimal feedback policy. We also establish the uniqueness of the vector of dual variables. These results become useful for the characterization and computation of optimal solutions. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free