Exhaustion of Resources: a Marked Temporal Process Framework

This paper deals with the exhaustion of a replenishable resource, one of the main topics in environ- mental research. To examine this problem, we construct a mechanism to estimate the probability of depletion under a very small set of assumptions. The stock of the resource is assumed to evolve accordingly to a marked temporal pro- cess generated by the shocks occurring in the environment. Our setting is eminently theoretical, and constitutes an effective extension of some important models of stochastic growth regarding sustainability and ruin analysis. Further- more, the validity of the model is supported through the evidence relative to the paradigmatic cases of water resource planning and oil reserves.