Dynamic optimization and Skiba sets in economic examples

Beyn W-J, Pampel T, Semmler W (2001)
Optimal Control Applications & Methods 22(5-6): 251-280.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
Abstract / Bemerkung
We discuss two optimization problems from economics. The first is a model of optimal investment and the second is a model of resource management. In both cases the time horizon is infinite and the optimal control variables are continuous. Typically, in these optimal control problems multiple steady states and periodic orbits occur. This leads to multiple solutions of the state-costate system each of which relates to a locally optimal strategy but has its own limiting behaviour (stationary or periodic). Initial states that allow different optimal solutions with the same value of the objective function are called Skiba points. The set of Skiba points is of interest, because it provides thresholds for a global change of optimal strategies. We provide a systematic numerical method for calculating locally optimal solutions and Skiba points via boundary value problems. In parametric or higher dimensional systems Skiba curves (or manifolds) appear and we show how to follow them by a continuation process. We apply our method to the models above where Skiba sets consist of points or curves and where optimal solutions have different stationary or periodic asymptotic behaviour. Copyright (C) 2001 John Wiley Sons, Ltd.
Erscheinungsjahr
Zeitschriftentitel
Optimal Control Applications & Methods
Band
22
Ausgabe
5-6
Seite(n)
251-280
ISSN
PUB-ID

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Beyn W-J, Pampel T, Semmler W. Dynamic optimization and Skiba sets in economic examples. Optimal Control Applications & Methods. 2001;22(5-6):251-280.
Beyn, W. - J., Pampel, T., & Semmler, W. (2001). Dynamic optimization and Skiba sets in economic examples. Optimal Control Applications & Methods, 22(5-6), 251-280. doi:10.1002/oca.696
Beyn, W. - J., Pampel, T., and Semmler, W. (2001). Dynamic optimization and Skiba sets in economic examples. Optimal Control Applications & Methods 22, 251-280.
Beyn, W.-J., Pampel, T., & Semmler, W., 2001. Dynamic optimization and Skiba sets in economic examples. Optimal Control Applications & Methods, 22(5-6), p 251-280.
W.-J. Beyn, T. Pampel, and W. Semmler, “Dynamic optimization and Skiba sets in economic examples”, Optimal Control Applications & Methods, vol. 22, 2001, pp. 251-280.
Beyn, W.-J., Pampel, T., Semmler, W.: Dynamic optimization and Skiba sets in economic examples. Optimal Control Applications & Methods. 22, 251-280 (2001).
Beyn, Wolf-Jürgen, Pampel, Thorsten, and Semmler, Willi. “Dynamic optimization and Skiba sets in economic examples”. Optimal Control Applications & Methods 22.5-6 (2001): 251-280.