Abstract
This paper considers a dynamic model of the firm in which the firm has debt financing as an additional means to provide funds for investments. It is assumed that it is more difficult for the firm to get a loan when the debt-equity ratio is large. Consequently it is imposed that the interest rate increases with this ratio. The model under consideration has been studied before by Steigum (1983, Econometrica). He obtained that the problem reduces to a strictly concave optimal control problem with a unique saddle point. In this paper we prove this result in a different way, and provide a generalization to his model by extending the objective functional such that positive utility is assigned to dividends as well as equity. Despite the fully concave setting, we show that the optimal solution of a mainly equity oriented firm has history dependent equilibria.
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Hartl, R.F., Kort, P.M., Novak, A. (2002). A Capital Accumulation Model with Debt Financing: The Steigum Model Revisited. In: Zaccour, G. (eds) Optimal Control and Differential Games. Advances in Computational Management Science, vol 5. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-1047-5_2
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DOI: https://doi.org/10.1007/978-1-4615-1047-5_2
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