Differentiability of the value function in continuous-time economic models Articles uri icon

publication date

  • June 2012

start page

  • 305

end page

  • 323

issue

  • 1

volume

  • 394

international standard serial number (ISSN)

  • 0022-247X

electronic international standard serial number (EISSN)

  • 1096-0813

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.