Exact finite approximations of average-cost countable Markov Decision Processes

For a countable-state Markov decision process we introduce an embedding which produces a finite-state Markov decision process. The finite-state embedded process has the same optimal cost, and moreover, it has the same dynamics as the original process when restricting to the approximating set. The embedded process can be used as an approximation which, being finite, is more convenient for computation and implementation.Comment: Submitted to Automatic

Resource Management with Stochastic Recharge and Environmental Threats

Exploitation diminishes the capacity of renewable resources to with-stand 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 (environmental threat) and 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 analyzed optimal resource management in such a setting. Existence of an optimal stationary policy is established and long run properties are characterized. A numerical illustration based on actual data is presented.Stochastic stock dynamics, event uncertainty, Markov decision process, optimal stationary policy, Environmental Economics and Policy,

DYNAMIC-SPATIAL MANAGEMENT OF COASTAL AQUIFERS

We analyze the management of a coastal aquifer under seawater intrusion using distributed control methods. The aquifer's state is taken as the water head elevation, which varies with time and in space since extraction, natural recharge and lateral water flows vary with time and in space. The water head, in turn, induces a temporal-spatial seawater intrusion process, which changes the volume of fresh water in the aquifer. Under reasonable conditions we show that the optimal state converges to a steady state process that is constant in time. We characterize the optimal steady state process in terms of a standard control problem (in space) and offer a tractable algorithm to solve for it.distributed control, groundwater, optimal exploitation, seawater intrusion, Resource /Energy Economics and Policy, C61, C62, Q25,

Controling Diffusion Processes on Infinite Horizon with the Overtaking Criterion

Leizarowitz, Arie. (1986). Controling Diffusion Processes on Infinite Horizon with the Overtaking Criterion. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/4334

Control Problems with Random and Progressively Known Target

Leizarowitz, Arie. (1986). Control Problems with Random and Progressively Known Target. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/4286