Skiba points in free end-time problems

J.P. Caulkins, G. Feichtinger, D. Grass, R.F. Hartl, Peter Kort, A. Seidl

Research output: Contribution to journalArticleScientificpeer-review

Abstract

Since the end of the seventies Skiba points have been studied in infinite time optimal control problems with multiple steady states. At such a Skiba point the decision maker is indifferent between choosing trajectories that approach different steady states. This paper extends this theory towards free end-time optimal control problems, where the decision maker collects a salvage value at the endogenous horizon date. In particular, besides operating forever, the decision maker can choose to stop operations immediately, or to operate during a finite time interval after which the decision maker stops and collects a salvage value.

This paper illustrates the new theory with a firm-level capital accumulation problem in which the manager has the option to sell the firm (be acquired) at any time. This situation may be relevant for certain high-tech start-ups that create intellectual property which may be of value to an acquiring firm and which is hard for an outside firm to tap in other ways (e.g., via licensing).
Original languageEnglish
Pages (from-to)404-419
JournalJournal of Economic Dynamics and Control
Volume51
DOIs
Publication statusPublished - Feb 2015

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Salvaging
Time-optimal Control
Intellectual property
Optimal Control Problem
Managers
Trajectories
Capital Accumulation
Intellectual Property
Date
Immediately
Horizon
Choose
Trajectory
Interval
Business
Decision maker
Optimal control

Keywords

  • optimal control
  • Skiba point
  • capital accumulation model
  • free end-time problem
  • takeover

Cite this

Caulkins, J. P., Feichtinger, G., Grass, D., Hartl, R. F., Kort, P., & Seidl, A. (2015). Skiba points in free end-time problems. Journal of Economic Dynamics and Control, 51, 404-419. https://doi.org/10.1016/j.jedc.2014.11.003
Caulkins, J.P. ; Feichtinger, G. ; Grass, D. ; Hartl, R.F. ; Kort, Peter ; Seidl, A. / Skiba points in free end-time problems. In: Journal of Economic Dynamics and Control. 2015 ; Vol. 51. pp. 404-419.
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Caulkins, JP, Feichtinger, G, Grass, D, Hartl, RF, Kort, P & Seidl, A 2015, 'Skiba points in free end-time problems', Journal of Economic Dynamics and Control, vol. 51, pp. 404-419. https://doi.org/10.1016/j.jedc.2014.11.003

Skiba points in free end-time problems. / Caulkins, J.P.; Feichtinger, G.; Grass, D.; Hartl, R.F.; Kort, Peter; Seidl, A.

In: Journal of Economic Dynamics and Control, Vol. 51, 02.2015, p. 404-419.

Research output: Contribution to journalArticleScientificpeer-review

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