The paper presents an analytic approximation for computing (s, S) policies for single items under periodic review with fixed ordering costs, linear holding costs and a service level requirement. The replenishment lead time is fixed and unfilled demand is backlogged. The approximation is similar...

In this paper, we apply the idea of $k$-local contraction of \cite{zec, zet} to study discounted stochastic dynamic programming models with unbounded returns. Our main results concern the existence of a unique solution to the Bellman equation and are applied to the theory of stochastic optimal...

A numerical dynamic model is developed to characterize the decision problem of a rancher operating on rangelands in northern Nevada that are affected by invasive annual grasses and wildfire. The model incorporates decisions about herd size management of a cow-calf operation and fuels treatment...

In this paper a stochastic dynamic game formulation of the economics of international environmental agreements on the transnational pollution control, when the environmental damage arises from stock pollutant that accumulates, for accumulating pollutants such as CO2 in the atmosphere is...

In this paper we discuss the costate variable in a stochastic optimal control model of a renewable natural resource, which we call a fishery. The role of the costate variable in deterministic control models has been discussed extensively in the literature. See, for example, Lyon (1999), Clark...

We consider an optimally managed renewable resource with stochastic non-concave growth function. We characterize the conditions under which the optimal policy leads to global extinction, global conservation and the existence of a safe standard of conservation. Our conditions are specified in...

This paper builds on our previous work that used a non linear stochastic dynamic programming problem to solve for the optimal level of phosphorus discharged into a watershed. Typically, there is a trade off between profits from agriculture and environmental damage due to excessive levels of...

In this paper we extend the deterministic model of Dechert and Brock (forthcoming) to stochastic models. First, we consider the lake game in a Brock and Mirman framework and show what happens to the Skiba point when there is uncertainty in the model. Second, we develop the model as an optimally...

Long-term observers of urban communities know that the housing quality distributions of communities and the changes of these distributions over time encompass not one but a variety of patterns. The equilibrium outcome derived from the housing market literature explains one pattern of change....