Differentiability of the value function in continuous-time economic models

Juan Pablo Rincón-Zapatero, Manuel Santos

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)305-323
Number of pages19
JournalJournal of Mathematical Analysis and Applications
Volume394
Issue number1
DOIs
StatePublished - Oct 1 2012

Fingerprint

Continuous-time Model
Economic Model
Differentiability
Value Function
Bellman Equation
Economics
Optimal Path
Convex optimization
Infinite Horizon
Constrained optimization
Constrained Optimization
Convex Optimization
Interior
Uniqueness
Optimal Solution
Feedback
Sufficient Conditions
Policy
Class

Keywords

  • Constrained optimization
  • Differentiability
  • Duality theory
  • Envelope theorem
  • Value function

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Differentiability of the value function in continuous-time economic models. / Rincón-Zapatero, Juan Pablo; Santos, Manuel.

In: Journal of Mathematical Analysis and Applications, Vol. 394, No. 1, 01.10.2012, p. 305-323.

Research output: Contribution to journalArticle

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