Financing policies via stochastic control: a dynamic programming approach

This is a post-peer-review, pre-copyedit version of an article published in the Journal of Global Optimization. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10898-011-9725-y 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.