Skiba points in free end time problems: the option to sell the firm

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 it stops and collects the salvage value. This paper partly develops the new theory by analyzing a capital accumulation problem of the firm where the manager has the option to sell the firm at any time. This problem is relevant especially in the high tech sector.

[1]  Gustav Feichtinger,et al.  Optimale Kontrolle ökonomischer Prozesse : Anwendungen des Maximumprinzips in den Wirtschaftswissenschaften , 1986 .

[2]  R. Hartl,et al.  Optimal investments with increasing returns to scale: A further analysis , 2000 .

[3]  A. Skiba,et al.  Optimal Growth with a Convex-Concave Production Function , 1978 .

[4]  Emilio Barucci,et al.  Optimal Investments with Increasing Returns to Scale , 1998 .

[5]  Suresh P. Sethi,et al.  Optimal advertising policy with the contagion model , 1979 .

[6]  Kazuo Nishimura,et al.  A Complete Characterization of Optimal Growth Paths in an Aggregated Model with a Non-Concave Production Function , 1983 .

[7]  Suresh P. Sethi,et al.  Nearest feasible paths in optimal control problems: Theory, examples, and counterexamples , 1977 .

[8]  D. Jorgenson.  Capital Theory and Investment Behavior , 1963 .

[9]  Richard F. Hartl,et al.  A simple proof of the monotonicity of the state trajectories in autonomous control problems , 1987 .

[10]  Peter M. Kort,et al.  Optimal investments with convex-concave revenue : A focus-node distinction , 2004 .

[11]  Peter M. Kort,et al.  Anticipation effects of technological progress on capital accumulation: a vintage capital approach , 2006, J. Econ. Theory.

[12]  J. Caulkins,et al.  Optimal Control of Nonlinear Processes: With Applications in Drugs, Corruption, and Terror , 2008 .

[13]  J. P. Gould.  Adjustment Costs in the Theory of Investment of the Firm , 1968 .