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Envelope theorems for non-smooth and non-concave optimization

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  • Andrew Clausen
  • Carlo Strub

Abstract

We study general dynamic programming problems with continuous and discrete choices and general constraints. The value functions may have kinks arising (1) at indifference points between discrete choices and (2) at constraint boundaries. Nevertheless, we establish a general envelope theorem: first-order conditions are necessary at interior optimal choices. We only assume differentiability of the utility function with respect to the continuous choices. The continuous choice may be from any Banach space and the discrete choice from any non-empty set.

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Bibliographic Info

Paper provided by Department of Economics - University of Zurich in its series ECON - Working Papers with number 062.

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Date of creation: Apr 2012
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Handle: RePEc:zur:econwp:062

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Related research

Keywords: Envelope theorem; differentiability; dynamic programming; discrete choice; non-smooth analysis;

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Cited by:
  1. Shouyong Shi & Hongfei Sun & Guido Menzio, 2009. "Monetary Theory with Non-degenerate Distributions," 2009 Meeting Papers 172, Society for Economic Dynamics.
  2. Giulio Fella, 2011. "A Generalized Endogenous Grid Method for Non-concave Problems," Working Papers 677, Queen Mary, University of London, School of Economics and Finance.
  3. Andrew Clausen (University of Edinburgh), 2013. "Moral Hazard with Counterfeit Signals," ESE Discussion Papers 225, Edinburgh School of Economics, University of Edinburgh.
  4. Andrew Clausen & Carlo Strub, 2011. "Money cycles," ECON - Working Papers 008, Department of Economics - University of Zurich.
  5. Christoph Görtz & Afrasiab Mirza, 2014. "On the Applicability of Global Approximation Methods for Models with Jump Discontinuities in Policy Functions," CESifo Working Paper Series 4837, CESifo Group Munich.
  6. Giulio Fella, 2014. "A generalized endogenous grid method for non-smooth and non-concave problems," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 17(2), pages 329-344, April.
  7. Chen, Daphne & Qi, Shi & Schlagenhauf, Don E., 2014. "Corporate income tax, legal form of organization, and employment," Working Papers 2014-18, Federal Reserve Bank of St. Louis.

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