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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; 404 - 419.

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).

http://dx.doi.org/10.1016/j.jedc.2014.11.003

http://www.sciencedirect.com/science/article/pii/S0165188914003005