Risky (Natural) Assets: Stochasticity, Nonconvexity, and the Value of Natural Capital

There is renewed interest in valuing the natural assets that sustain human welfare and economic prosperity. The science associated with many renewable natural asset stocks often highlights risk, uncertainty, and tipping points (nonconvexities). However, there is little guidance in the literature concerning how to incorporate risk or tipping points within capital dynamics into the valuation of nonmarket assets. We extend and demonstrate the theory of natural capital valuation for smooth stochasticity (diffusions) with convex and nonconvex drift terms and for “stochastic nonconvexities,” whereby a stock is subject to endogenous risk of collapse. We highlight pathways for risk to influence capital valuations, demonstrating conditions where diffusions with convex dynamics have negligible effects on shadow prices. However, we find that risk has large stock-dependent effects in the context of nonconvexities. Our findings suggest that efforts to incorporate risk into natural capital valuation should prioritize settings where nonconvex capital dynamics are likely.