Conventional wisdom states that incentives targeting stocks and flows can lead to equivalent externalities correction. However, this may not hold when externalities are directly produced from stocks of capital ("stock-generated externalities") rather than flows of production. Privately-owned stocks that exhibit external effects include trees with respect to CO2 absorption, shellfish and water cleaning, and livestock and methane emissions. I present an optimal control model of externality-correcting incentives to compare policies targeting measures of stocks and flows. The setting focuses on an extractive firm which privately owns a renewable stock where joint production of a private good and social benefits occurs. I compare the theoretical performance of stock and flow policies in steady state to the social optimum and a no-policy benchmark. The model is then calibrated to industry and scientific parameters of Eastern oyster (C. virginica) production in the Chesapeake Bay, where shellfish cultivation yields water filtration benefits, to explore short run dynamics. Overall, stock-targeted incentives can achieve the socially optimal allocations of resource abundance and environmental quality in steady state. While flow-targeting may yield short run benefits, the allocations become no different than no-policy in the long run. The lack of long run efficacy from flow-targeting is likely driven by revenue constraints that disallow the firm to increase stock abundance to a substantial degree across time. This paper presents a theory of incentive design aimed at minimizing environmental damages through management of privately-owned renewable natural resources.