Abstract
We consider a mathematical model, posed by J.E. Scheinkman, simulating that an industrial project takes place into the environment without destroying it. We introduce a change of variable leading the formulation to a nonlinear evolution problem which we study by means of L ∞ -accretive operator techniques. We prove that under suitable conditions there is extinction in finite time, which corresponds to some special behaviour of the solution of the original stochastic control problem.
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