Actions on Environment under uncertainty: stochastic formulation and the associated deterministic problem

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An application of the results of this paper proves that there is not always an economic benefit when destroying the environment for planting an alternative industrial project. Our criterion, to act, to delay or to deny the industrial investment over the environment, is given in terms of the free boundary associated to a deterministic degenerate obstacle problem (on an unbounded domain) associated to the stochastic optimal control problem formulated, initially, in terms of some suitable stochastic diffusion processes. The localizing estimates on the free boundary are obtained through a suitable spatial change of variables and by working with a suitable distance associated to the coefficient of the elliptic operator.


Una interpretación de los resultados de este trabajo muestra que no siempre hay beneficio Económico cuando se destruye el medio ambiente para la implantación de un proyecto industrial alternativo. Nuestro criterio, de actuar, retrasar o negar la inverseón industrial sobre el medio ambiente, viene dado en términos de la frontera libre asociada a un problema de obstáculo determinista degenerado (sobre un dominio no acotado) asociado al problema estocástico de control óptimo formulado, inicialmente, en términos de ciertos procesos de difusión estocásticos.