# Regulation of renewable resource exploitation

## TL;DR

This paper models how regulation policies influence the exploitation of renewable resources using advanced mathematical tools, providing a framework to design effective contracts and analyze their impact on resource management.

## Contribution

It introduces a novel approach combining BSDE and HJB equations to characterize optimal regulation contracts under various conditions.

## Key findings

- Optimal contracts can be characterized via HJB equations.
- Less regular coefficients and logistic dynamics are incorporated.
- Numerical examples demonstrate regulation impacts on resource exploitation.

## Abstract

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.