S. PASQUALI, W.J. RUNGGALDIER
Approximations of a controlled diffusion model for renewable
resource exploitation
Markov
Processes and Controlled Markov Chains
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.