IDEAS home Printed from https://ideas.repec.org/a/spr/dyngam/v4y2014i3p257-289.html
   My bibliography  Save this article

Robust Control and Hot Spots in Spatiotemporal Economic Systems

Author

Listed:
  • W. Brock
  • A. Xepapadeas
  • A. Yannacopoulos

Abstract

We formulate stochastic robust optimal control problems, motivated by applications arising in interconnected economic systems, or spatially extended economies. We study in detail linear quadratic problems and nonlinear problems. We derive optimal robust controls and identify conditions under which concerns about model misspecification at specific site(s) could cause regulation to break down, to be very costly, or to induce pattern formation and spatial clustering. We call sites associated with these phenomena hot spots. We also provide an application of our methods by studying optimal robust control and the potential break down of regulation, due to hot spots, in a model where utility for in situ consumption is distance dependent. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • W. Brock & A. Xepapadeas & A. Yannacopoulos, 2014. "Robust Control and Hot Spots in Spatiotemporal Economic Systems," Dynamic Games and Applications, Springer, vol. 4(3), pages 257-289, September.
    • Handle: RePEc:spr:dyngam:v:4:y:2014:i:3:p:257-289
    DOI: 10.1007/s13235-014-0109-z
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s13235-014-0109-z
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s13235-014-0109-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Control and Model Uncertainty," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 5, pages 145-154, World Scientific Publishing Co. Pte. Ltd..
    3. Boucekkine, Raouf & Camacho, Carmen & Zou, Benteng, 2009. "Bridging The Gap Between Growth Theory And The New Economic Geography: The Spatial Ramsey Model," Macroeconomic Dynamics, Cambridge University Press, vol. 13(1), pages 20-45, February.
    4. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Control and Model Misspecification," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 6, pages 155-216, World Scientific Publishing Co. Pte. Ltd..
    5. Lars Ljungqvist & Thomas J. Sargent, 2004. "Recursive Macroeconomic Theory, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 026212274x, April.
    6. Brock, William & Xepapadeas, Anastasios, 2010. "Pattern formation, spatial externalities and regulation in coupled economic-ecological systems," Journal of Environmental Economics and Management, Elsevier, vol. 59(2), pages 149-164, March.
    7. Stergios Athanassoglou & Anastasios Xepapadeas, 2011. "Pollution control: when, and how, to be precautious," DEOS Working Papers 1112, Athens University of Economics and Business.
    8. 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.
    9. Akamatsu, Takashi & Takayama, Yuki & Ikeda, Kiyohiro, 2012. "Spatial discounting, Fourier, and racetrack economy: A recipe for the analysis of spatial agglomeration models," Journal of Economic Dynamics and Control, Elsevier, vol. 36(11), pages 1729-1759.
    10. 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.
    11. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    12. Tony E. Smith, 1975. "An Axiomatic Theory Of Spatial Discounting Behavior," Papers in Regional Science, Wiley Blackwell, vol. 35(1), pages 31-43, January.
    13. Wu, JunJie & Plantinga, Andrew J., 2003. "The influence of public open space on urban spatial structure," Journal of Environmental Economics and Management, Elsevier, vol. 46(2), pages 288-309, September.
    14. Klaus Desmet & Esteban Rossi‐Hansberg, 2010. "On Spatial Dynamics," Journal of Regional Science, Wiley Blackwell, vol. 50(1), pages 43-63, February.
    15. Lars Peter Hansen & Thomas J Sargent, 2014. "A Quartet of Semigroups for Model Specification, Robustness, Prices of Risk, and Model Detection," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 4, pages 83-143, World Scientific Publishing Co. Pte. Ltd..
    16. Smith, Tony E., 1976. "Spatial discounting and the gravity hypothesis," Regional Science and Urban Economics, Elsevier, vol. 6(4), pages 331-356, December.
    17. Sanchirico, James N. & Wilen, James E., 1999. "Bioeconomics of Spatial Exploitation in a Patchy Environment," Journal of Environmental Economics and Management, Elsevier, vol. 37(2), pages 129-150, March.
    18. Paulo B. Brito, 2022. "The dynamics of growth and distribution in a spatially heterogeneous world," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 21(3), pages 311-350, September.
    19. Charles Perrings & Bruce Hannon, 2001. "An Introduction to Spatial Discounting," Journal of Regional Science, Wiley Blackwell, vol. 41(1), pages 23-38, February.
    20. Brock, William & Xepapadeas, Anastasios, 2008. "Diffusion-induced instability and pattern formation in infinite horizon recursive optimal control," Journal of Economic Dynamics and Control, Elsevier, vol. 32(9), pages 2745-2787, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Bondarev, Anton, 2018. "Robust policy schemes for R&D games with asymmetric information," Working papers 2018/01, Faculty of Business and Economics - University of Basel.
    2. William Brock & Anastasios Xepapadeas & Athanasios Yannacopoulos, 2014. "Spatiotemporal robust control in infinite dimensional spaces," DEOS Working Papers 1405, Athens University of Economics and Business.
    3. William A. Brock & Anastasios Xepapadeas & Athanasios N. Yannacopoulos, 2014. "Robust Control of a Spatially Distributed Commercial Fishery," Dynamic Modeling and Econometrics in Economics and Finance, in: Elke Moser & Willi Semmler & Gernot Tragler & Vladimir M. Veliov (ed.), Dynamic Optimization in Environmental Economics, edition 127, pages 215-241, Springer.
    4. Athanasios Yannacopoulos & Anastasios Xepapadeas, 2013. "Climate Change Policy under Spatially Structured Ambiguity: Hot Spots and the Precautionary Principle," DEOS Working Papers 1332, Athens University of Economics and Business.
    5. Anton Bondarev, 2019. "Robust Policy Schemes for Differential R&D Games with Asymmetric Information," Dynamic Games and Applications, Springer, vol. 9(2), pages 391-415, June.
    6. Bondarev, Anton & Krysiak, Frank C., 2017. "Temporary and permanent technology lock-ins in the quality-differentiated Bertrand competition," Working papers 2017/09, Faculty of Business and Economics - University of Basel.
    7. Anastasios Xepapadeas & Athanasios Yannacopoulos, 2018. "Spatially Structured Deep Uncertainty, Robust Control, and Climate Change Policies," DEOS Working Papers 1807, Athens University of Economics and Business.
    8. Anton Bondarev & Frank C. Krysiak, 2017. "Robust policy schemes for R&D games with asymmetric information," Working papers 2017/14, Faculty of Business and Economics - University of Basel.
    9. Phoebe Koundouri & Georgios I. Papayiannis & Athanasios Yannacopoulos, 2022. "Optimal Control Approaches to Sustainability under Uncertainty," DEOS Working Papers 2215, Athens University of Economics and Business.
    10. Baltas, I. & Dopierala, L. & Kolodziejczyk, K. & Szczepański, M. & Weber, G.-W. & Yannacopoulos, A.N., 2022. "Optimal management of defined contribution pension funds under the effect of inflation, mortality and uncertainty," European Journal of Operational Research, Elsevier, vol. 298(3), pages 1162-1174.
    11. Georgios I. Papayiannis, 2022. "Robust Policy Selection and Harvest Risk Quantification for Natural Resources Management under Model Uncertainty," Papers 2202.05326, arXiv.org.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. W. A. Brock & A. Xepapadeas, 2015. "Modeling Coupled Climate, Ecosystems, and Economic Systems," Working Papers 2015.66, Fondazione Eni Enrico Mattei.
    2. W.A. Brock & A. Xepapadeas & A.N. Yannacopoulos, 2014. "Optimal Control in Space and Time and the Management of Environmental Resources," Annual Review of Resource Economics, Annual Reviews, vol. 6(1), pages 33-68, October.
    3. William A. Brock & Anastasios Xepapadeas & Athanasios N. Yannacopoulos, 2014. "Robust Control of a Spatially Distributed Commercial Fishery," Dynamic Modeling and Econometrics in Economics and Finance, in: Elke Moser & Willi Semmler & Gernot Tragler & Vladimir M. Veliov (ed.), Dynamic Optimization in Environmental Economics, edition 127, pages 215-241, Springer.
    4. Camacho, Carmen & Pérez-Barahona, Agustín, 2015. "Land use dynamics and the environment," Journal of Economic Dynamics and Control, Elsevier, vol. 52(C), pages 96-118.
    5. William Brock & Anastasios Xepapadeas, 2020. "Spatial Environmental and Resource Economics," DEOS Working Papers 2002, Athens University of Economics and Business.
    6. Anastasios Xepapadeas, 2012. "Diffusion and Spatial Aspects," DEOS Working Papers 1232, Athens University of Economics and Business.
    7. Rintaro Yamaguchi, 2021. "Genuine Savings and Sustainability with Resource Diffusion," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 80(2), pages 451-471, October.
    8. Lars Peter Hansen & Thomas J Sargent, 2014. "Three Types of Ambiguity," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 11, pages 379-430, World Scientific Publishing Co. Pte. Ltd..
    9. Xepapadeas, Anastasios & Yannacopoulos, Athanasios N., 2023. "Spatial growth theory: Optimality and spatial heterogeneity," Journal of Economic Dynamics and Control, Elsevier, vol. 146(C).
    10. Zhang, Jinqing & Jin, Zeyu & An, Yunbi, 2017. "Dynamic portfolio optimization with ambiguity aversion," Journal of Banking & Finance, Elsevier, vol. 79(C), pages 95-109.
    11. Anastasios Xepapadeas, 2010. "Modeling complex systems," Agricultural Economics, International Association of Agricultural Economists, vol. 41(s1), pages 181-191, November.
    12. Chen, Yong & Irwin, Elena G. & Jayaprakash, Ciriyam, 2011. "Incorporating Spatial Complexity into Economic Models of Land Markets and Land Use Change," Agricultural and Resource Economics Review, Northeastern Agricultural and Resource Economics Association, vol. 40(3), pages 1-20, December.
    13. William Brock & Anastasios Xepapadeas & Athanasios Yannacopoulos, 2014. "Spatiotemporal robust control in infinite dimensional spaces," DEOS Working Papers 1405, Athens University of Economics and Business.
    14. David Aadland & Charles Sims & David Finnoff, 2015. "Spatial Dynamics of Optimal Management in Bioeconomic Systems," Computational Economics, Springer;Society for Computational Economics, vol. 45(4), pages 545-577, April.
    15. de Frutos, Javier & Martín-Herrán, Guiomar, 2019. "Spatial vs. non-spatial transboundary pollution control in a class of cooperative and non-cooperative dynamic games," European Journal of Operational Research, Elsevier, vol. 276(1), pages 379-394.
    16. Xepapadeas, A. & Yannacopoulos, A.N., 2016. "Spatial growth with exogenous saving rates," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 125-137.
    17. Hansen, Lars Peter & Sargent, Thomas J., 2022. "Structured ambiguity and model misspecification," Journal of Economic Theory, Elsevier, vol. 199(C).
    18. Karantounias, Anastasios G., 2023. "Doubts about the model and optimal policy," Journal of Economic Theory, Elsevier, vol. 210(C).
    19. Aït-Sahalia, Yacine & Matthys, Felix, 2019. "Robust consumption and portfolio policies when asset prices can jump," Journal of Economic Theory, Elsevier, vol. 179(C), pages 1-56.
    20. Agliardi, Elettra & Xepapadeas, Anastasios, 2022. "Temperature targets, deep uncertainty and extreme events in the design of optimal climate policy," Journal of Economic Dynamics and Control, Elsevier, vol. 139(C).

    More about this item

    Keywords

    Stochastic control; Robust control; Riccati equation; Hot spot formation; Pattern formation; Hamilton-Jacobi Bellman equation; Distance-dependent utility; C6; R12; Q26;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)
    • Q26 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - Recreational Aspects of Natural Resources

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:dyngam:v:4:y:2014:i:3:p:257-289. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.