Díaz Díaz, Jesús IldefonsoFaghloumi, Ch.2023-06-202023-06-202002Arnold, L. (1974), Stochastic Differential Equations: Theory and Applications, Wiley, New York. Aziz, A. K., and Balas, M. J. (1977), Control Theory of Systems Governed by Partial Differential Equations, Academic Press, London. Bellman, R. (1957), Dynamic Programing, Academic Press, London. Bensoussan, A., and Lions, J. L. (1978), Application des inégalités variationnelles en control stochastique, Dunod, Paris. Bensoussan, A. (1982), Stochastic Control by Functional Analysis Methods, North-Holland, Amsterdam. Bensoussan, A., and Lions, J. L. (1976), On the support of the solution of some variational inequalities of evolution, J. Math. Soc. Japan, 28(1):1–17. Bermudez, A., Moreno, C., and Sanmartin, A. (1997), Resolución numérica de un problema de valor óptimo de una opción, in Actas de la Jornada Científica en homenaje a A. Valle, T. Caraballo et al., eds., Publicaciones de la Universidad de Sevilla, pp. 201–214. Brezis, H. (1972), Problèmes Unilateraux, J. Math. Pures Appl., 51:1–168. Brezis, H. (1983), Analyse fonctionelle, Masson, Paris. Brezis, H., and Friedman, A. (1976), Estimates on the support of the solutions of parabolic variational inequalities, Illinois J. Math., 20:82–97. Crandall, M. G., Ishii, H., and Lions, P. L. (1992), User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc., 27:1–67. Dasgupa, P. P., Hammond, M., and Meskin, E. (1980), On imperfect information and optimal pollution control, Rev. Econom. Stud., 857–860. Díaz, J. I. (1985), Nonlinear Partial Differential Equations and Free Boundaries, Pitman, London. Dixit, A. K., and Pindyck, R.S. (1994), Investment under Uncertainty, Princeton University Press, Princeton, NJ. Fleming, W. H., and Rishel, R. (1975), Deterministic and Stochastic Optimal Control, Springer-Verlag, New York. Friedman, A. (1979), Stochastic Differential Equations, Holt, Rinehart and Winston, New York. Friedman, A. (1982), Variational Principles and Free Boundary Problems, Wiley, New York. Herbelot, O. (1992), Option Valuation of Flexible Investments: The Case of Environmental Investments in the Electric Power Industry, Ph.D., M.I.T., Massachusetts. Ito, K. (1951), On stochastic differential equations, Memoirs Amer. Math. Soc., No. 4, New York. Ito, K. and McKain, H. P. (1974), Diffusion Processes and Their Sample Paths, Springer-Verlag, Berlin. Krilov, N. V. (1972), On control of the solution of stochastic integral equation with degeneration, Math. USSR-Iz., 6:249–262. Kwerel, E. (1977), To tell the truth: imperfect information and optimal pollution control, Rev. Econom. Stud., 585–601. Pindyck, R. S. (1986), Irreversible investments, capacity choice and the value of the firm, Amer. Econom. Rev., 78:707–728. Scheinkman, J. A. (1994), Public goods and the environment, in Environment Economics and Their Mathematical Models, J. I. Díaz and J. L. Lions, eds., Masson, Paris, pp. 149–158. Scheinkman, J. A., and Zariphopoulou, Th. (to appear), Optimal environmental management in the presence of irreversibilities. Troianiello, G. M. (1987), Elliptic Differential Equations and Obstacle Problems, Plenum, New York.0095-461610.1007/s00245-001-0038-2https://hdl.handle.net/20.500.14352/57326We study a class of optimization dynamics problems related to investment under uncertainty. The general model problem is reformulated in terms of an obstacle problem associated to a second-order elliptic operator which is not in divergence form. The spatial domain is unbounded and no boundary conditions are a priori specified. By using the special structure of the differential operator and the spatial domain, and some approximating arguments, we show the existence and uniqueness of a solution of the problem. We also study the regularity of the solution and give some estimates on the location of the coincidence set.engjournal articlehttp://www.springerlink.com/content/h4t9a3t0jq7peatm/fulltext.pdfhttp://www.springerlink.com/restricted access517.954elliptic free boundarydegenerate operatorunbounded domainenvironmental policyGeometría diferencialEcuaciones diferenciales1204.04 Geometría Diferencial1202.07 Ecuaciones en Diferencias