Renewable resource management with stochastic recharge and environmental threats

Exploitation diminishes the capacity of renewable resources to withstand environmental stress, increasing their vulnerability to extreme conditions that may trigger abrupt changes. The onset of such events depends on the coincidence of extreme environmental conditions and on the resource state (determining its resilience). When the former is uncertain and the latter evolves stochastically, the uncertainty regarding the event occurrence is the result of the combined effect of these two uncertain components. We study optimal management in this setting. The environmental threat renders the single-period discount factor policy-dependent and, as a result, the compound discount factor becomes history-dependent. Existence of an optimal Markovian-deterministic stationary policy is established and the optimal state process is shown to converge to a steady state distribution.