Financing policies via stochastic control: a dynamic programming approach

This paper deals with a theoretical stochastic dynamic optimization model for the external financing of firms. We aim at searching for the best intensity of payment that a financier has to apply to a company in order to have a loan repaid. The techniques involved are related to the optimal control theory with exit time. We follow a dynamic programming approach. Our model also presents a distinction between the legal and the illegal financier, and a theoretical comparison analysis of the results is presented. Some numerical examples provide further validation of the theoretical results.