A Maximum Principle for Control Problems with Monotonicity Constraints

Hellwig, Martin F.

doi:10.2139/ssrn.1101438

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A Maximum Principle for Control Problems with Monotonicity Constraints

MPI Collective Goods Preprint, No. 2008/4

39 Pages Posted: 4 Mar 2008 Last revised: 13 Aug 2009

See all articles by Martin F. Hellwig

Martin F. Hellwig

Max Planck Institute for Research on Collective Goods; University of Bonn - Department of Economics; European Corporate Governance Institute (ECGI)

Date Written: February 1, 2008

Abstract

The paper develops a version of Pontryagin's maximum principle for optimal control problems with monotonicity constraints on control variables. Whereas the literature handles such constraints by imposing an assumption of piecewise smoothness on the control variable and treating the slope of this variable as a new control variable subject to a non-negativity constraint, the paper obtains the maximum principle without such an additional assumption. The result is useful for studying incentive problems with hidden characteristics when the type set is a continuum and preferences satisfy a single-crossing constraint.

Keywords: Maximum Principle, Optimal Control, Monotonicity Constraints, Incentive Problems with Hidden Characteristics

JEL Classification: C61

Suggested Citation: Suggested Citation

Hellwig, Martin F., A Maximum Principle for Control Problems with Monotonicity Constraints (February 1, 2008). MPI Collective Goods Preprint, No. 2008/4, Available at SSRN: https://ssrn.com/abstract=1101438 or http://dx.doi.org/10.2139/ssrn.1101438