Stochastic Shadow Pricing of Renewable Natural Resources

By means of stochastic optimal control, this paper aims at studying the shadow pricing of renewable natural resources in uncertainty. Two cases are considered, respectively centralized and decentralized control processes. The decentralized control is in the form of a stochastic control of the state vector distributed among several agents. In both cases, the optimal control path minimizing the cost function, which is a decreasing function of time, corresponds to the real option valuation. The latter is a cost-effective optional investment in the resource stock preservation in uncertainty. The results obtained from numerical simulations show coherence with those encountered in the literature on option pricing.