Actions on Environment under uncertainty: stochastic formulation and the associated deterministic problem
| dc.contributor.author | Díaz Díaz, Jesús Ildefonso | |
| dc.contributor.author | Faghloumi, Ch. | |
| dc.date.accessioned | 2023-06-20T09:34:12Z | |
| dc.date.available | 2023-06-20T09:34:12Z | |
| dc.date.issued | 2008 | |
| dc.description.abstract | 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 in 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. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | DGISGP (Spain) | |
| dc.description.sponsorship | CAM | |
| dc.description.sponsorship | UCM | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/15247 | |
| dc.identifier.doi | 10.1007/BF03191827 | |
| dc.identifier.issn | 1578-7303 | |
| dc.identifier.officialurl | http://www.springerlink.com/content/x658372165l07n2k/ | |
| dc.identifier.relatedurl | http://www.springerlink.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/49929 | |
| dc.issue.number | 2 | |
| dc.journal.title | Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A: Matemáticas | |
| dc.language.iso | eng | |
| dc.page.final | 353 | |
| dc.page.initial | 335 | |
| dc.publisher | Real Academia Ciencias Exactas Físicas Y Naturales | |
| dc.relation.projectID | MTM2005-03463 | |
| dc.relation.projectID | CCG07-UCM/ESP-2787 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 519.21 | |
| dc.subject.keyword | degenerate obstacle problem | |
| dc.subject.keyword | Unbounded domain | |
| dc.subject.keyword | stochastic optimal control problem | |
| dc.subject.keyword | environmental economy | |
| dc.subject.ucm | Estadística aplicada | |
| dc.subject.ucm | Procesos estocásticos | |
| dc.subject.unesco | 1208.08 Procesos Estocásticos | |
| dc.title | Actions on Environment under uncertainty: stochastic formulation and the associated deterministic problem | |
| dc.type | journal article | |
| dc.volume.number | 102 | |
| dcterms.references | AKERLOF, G. A. (1998), The Market for Lemons: Qualitative Uncertainty and the Market Mechanism, Quarterly Journal of Economics, 84, 488–500. BELLMAN, R. (1957), Dynamic Programming. Academic Press, London. BENSOUSSAN, A. AND LIONS, J. L., (1978). Application des inégalités variationnelles en control stochastique. Dunod, Paris. 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, Caraballo, T., et al Eds, Publicaciones de la Universidad de Sevilla. BREZIS, H., (1972). Problèmes Unilateraux. J. Math. Pures et Appl., 51, 1–168. BREZIS, H., (1983). Analyse fonctionnelle. 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. DÍAZ, G., (1985). Acción óptima en una ecuación de la Programación Dinámica. Rev. R. Acad. Cienc. Exactas Fís. Nat., LXXIX, 89–105. DÍAZ, G., DÍAZ, J. I., FAGHLOUMI C.,, (2007). On an evolution problem associated to the modelling of incertitude into the Environment. Nonlinear Analysis: Real World Applications, 8, 399–404. DÍAZ, J. I., (1985). Nonlinear partial differential equations and free boundaries. 106, Pitman, London. DÍAZ, J. I., FAGHLOUMI, C., (2002). Analysis of a nonlinear elliptic problem arising in the study of policies on projects altering the environment, Applied Math. and Optimization, 45, 251–267. DIXIT, A. K. AND PINDYCK, R. S., (1994). Investment under Uncertainly. Princeton University Press, Princeton. FAGHLOUMI, C., (2004). Modelizacion y tratamiento de algunos problemas de Medio Ambiente. Ph. D., thesis, Universidad Complutense de Madrid, Madrid. FLEMING, W. H. AND RISHEL, R. (1975). Deterministic and stochastic optimal control, Springer-Verlag, 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. KINDERLHERER, D. AND STAMPACCHIA, G., (2002). An introduction to Variational Inequalities and its Applications, Second edition, SIAM, Philadelphia. LIONS, J. L., (1969). Quelques méthodes de resolution des problémes aux limites non linearies, Dunod, París. OKSENDAL, B., (1998). Stochastic Differential Equations. Springer 5 th edition, Berlin. PINDYCK, R. S., (1986). Irreversible Investments, Capacity Choice and the Value of the Firm. American Economic Review, 78, 707–728. SCHEINKMAN, J. A., (1994). Public goods and the Environment, in Environment Economics and their Mathematical Models, Díaz, J. I. and Lions, J. L. Eds, Masson, Paris, 149–158. TROIANIELLO, G. M., (1987). Elliptic differential equations and obstacle problems. Plenum Press, New York. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 34ef57af-1f9d-4cf3-85a8-6a4171b23557 | |
| relation.isAuthorOfPublication.latestForDiscovery | 34ef57af-1f9d-4cf3-85a8-6a4171b23557 |
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