We study the problem of a renewable resource exploitation as a problem of optimal stochastic control with the renewable resource being managed for social benefit.
The aim is to maximize finte horizon total discounted utility by controlling per capita consumption and extraction capacity. We suppose the state is not directly observable, so we have an optimal stochastic control problem with partial observations.
The exact solution is difficult to obtain, so we aim at a nearly optimal control determined via an approximation approach involving a discretization procedure in time and space and leading thus to a Markovian decision problem.

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