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Optimal Control in Space and Time and the Management of Environmental Resources

  • William Brock
  • Anastasios Xepapadeas
  • Athanasios Yannacopoulos

We present methods and tools that can be used to study dynamic environmental resource management in a spatial setting, to explore spatially dependent regulation, and to understand pattern formation.In particular we present the maximum principle and its use in the context of the emerging frontier of applications of optimal control of diffusive transport processes to environmental and resource economics. We show how optimal spatiotemporal control induces pattern formation, and how deep uncertainty with a spatial structure can be handled with spatial robust control methods. Finally we show how models with diffusive transport can be extended to allow for long-range effects and more general transport mechanisms.

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Paper provided by Athens University of Economics and Business in its series DEOS Working Papers with number 1402.

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Date of creation: 16 Feb 2014
Date of revision:
Handle: RePEc:aue:wpaper:1402
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  1. Hansen, Lars Peter & Sargent, Thomas J., 2003. "Robust control of forward-looking models," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 581-604, April.
  2. Hassler, John & Krusell, Per, 2012. "Economics and Climate Change: Integrated Assessment in a Multi-Region World," CEPR Discussion Papers 8771, C.E.P.R. Discussion Papers.
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  5. Camacho, Carmen & Zou, Benteng & Briani, Maya, 2008. "On the dynamics of capital accumulation across space," European Journal of Operational Research, Elsevier, vol. 186(2), pages 451-465, April.
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  8. Brito, Paulo, 2011. "Global endogenous growth and distributional dynamics," MPRA Paper 41653, University Library of Munich, Germany.
  9. Carmen Camacho & Raouf Boucekkine & Fabbri Giorgio, 2013. "Spatial dynamics and convergence: The spatial AK model," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00973387, HAL.
  10. Klaus Desmet & Esteban Rossi-Hansberg, 2010. "On Spatial Dynamics," Journal of Regional Science, Wiley Blackwell, vol. 50(1), pages 43-63.
  11. Goetz, Renan U. & Zilberman, David, 2000. "The dynamics of spatial pollution: The case of phosphorus runoff from agricultural land," Journal of Economic Dynamics and Control, Elsevier, vol. 24(1), pages 143-163, January.
  12. Alexei Onatski & Noah Williams, 2003. "Modeling Model Uncertainty," NBER Working Papers 9566, National Bureau of Economic Research, Inc.
  13. Athanassoglou, Stergios & Xepapadeas, Anastasios, 2012. "Pollution control with uncertain stock dynamics: When, and how, to be precautious," Journal of Environmental Economics and Management, Elsevier, vol. 63(3), pages 304-320.
  14. Papageorgiou, Yorgo Y & Smith, Terrence R, 1983. "Agglomeration as Local Instability of Spatially Uniform Steady-States," Econometrica, Econometric Society, vol. 51(4), pages 1109-19, July.
  15. Pascal J. Maenhout, 2004. "Robust Portfolio Rules and Asset Pricing," Review of Financial Studies, Society for Financial Studies, vol. 17(4), pages 951-983.
  16. Itzhak Gilboa & David Schmeidler, 1989. "Maxmin Expected Utility with Non-Unique Prior," Post-Print hal-00753237, HAL.
  17. Brock, William & Xepapadeas, Anastasios, 2008. "Pattern Formation, Spatial Externalities and Regulation in Coupled Economic-Ecological Systems," MPRA Paper 9105, University Library of Munich, Germany.
  18. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, June.
  19. Benveniste, L. M. & Scheinkman, J. A., 1982. "Duality theory for dynamic optimization models of economics: The continuous time case," Journal of Economic Theory, Elsevier, vol. 27(1), pages 1-19, June.
  20. Desmet, Klaus & Rossi-Hansberg, Esteban, 2015. "On the spatial economic impact of global warming," Journal of Urban Economics, Elsevier, vol. 88(C), pages 16-37.
  21. Magill, Michael J. P., 1977. "A local analysis of N-sector capital accumulation under uncertainty," Journal of Economic Theory, Elsevier, vol. 15(1), pages 211-219, June.
  22. repec:cor:louvrp:-2449 is not listed on IDEAS
  23. Smith, Martin D. & Sanchirico, James N. & Wilen, James E., 2009. "The economics of spatial-dynamic processes: Applications to renewable resources," Journal of Environmental Economics and Management, Elsevier, vol. 57(1), pages 104-121, January.
  24. Brock, William A. & Engström, Gustav & Grass, Dieter & Xepapadeas, Anastasios, 2013. "Energy balance climate models and general equilibrium optimal mitigation policies," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2371-2396.
  25. Xabadia, M. Àngels & Goetz, Renan U. & Zilberman, David, 2004. "Spatially and Intertemporally Efficient Management of Waterlogging," Working Papers of the Department of Economics, University of Girona 9, Department of Economics, University of Girona.
  26. Giannis Vardas & Anastasios Xepapadeas, 2010. "Model Uncertainty, Ambiguity and the Precautionary Principle: Implications for Biodiversity Management," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 45(3), pages 379-404, March.
  27. Maenhout, Pascal J., 2006. "Robust portfolio rules and detection-error probabilities for a mean-reverting risk premium," Journal of Economic Theory, Elsevier, vol. 128(1), pages 136-163, May.
  28. Takao Asano, 2010. "Precautionary Principle and the Optimal Timing of Environmental Policy Under Ambiguity," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 47(2), pages 173-196, October.
  29. Catarina Roseta-Palma & Anastasios Xepapadeas, 2004. "Robust Control in Water Management," Journal of Risk and Uncertainty, Springer, vol. 29(1), pages 21-34, 07.
  30. James E. Wilen, 2007. "Economics of Spatial-Dynamic Processes," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 89(5), pages 1134-1144.
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