Regulation of renewable resource exploitation

We investigate the impact of a regulation policy imposed on an agent exploiting a possibly renewable natural resource. We adopt a principal-agent model in which the Principal looks for a contract, i.e. taxes/compensations, leading the Agent to a certain level of exploitation. For a given contract, we first describe the Agent's optimal harvest using the BSDE theory. Under regularity and boundedness assumptions on the coefficients, we express almost optimal contracts as solutions to HJB equations. We then extend the result to coefficients with less regularity and logistic dynamics for the natural resource. We end by numerical examples to illustrate the impact of the regulation in our model.