A viability theory approach to a two-stage optimal control problem

Jacek Krawczyk () and Oana-Silvia Serea

MPRA Paper from University Library of Munich, Germany

Abstract: A two-stage control problem is one, in which model parameters (“technology”) might be changed at some time. An optimal solution to utility maximisation for this class of problems needs to thus contain information on the time, at which the change will take place (0, finite or never) as well as the optimal control strategies before and after the change. For the change, or switch, to occur the “new technology” value function needs to dominate the “old technology” value function, after the switch. We charaterise the value function using the fact that its hypograph is a viability kernel of an auxiliary problem and study when the graphs can intersect and hence whether the switch can occur. Using this characterisation we analyse a technology switching problem.

Keywords: value function; viability kernel; viscosity solutions (search for similar items in EconPapers)
JEL-codes: C61 C69 (search for similar items in EconPapers)
Date: 2007-12-12
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Citations: View citations in EconPapers (3)

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