J. P. Caulkins, G. Feichtinger, D. Grass, R.F. Hartl, P.M. Kort, A. Seidl:
"Skiba Points in Free End-time Problems";
Journal of Economic Dynamics & Control, 51 (2015), 1; S. 404 - 419.

Kurzfassung englisch:
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).

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