Dynamic Games and Applications

, Volume 4, Issue 3, pp 257–289 | Cite as

Robust Control and Hot Spots in Spatiotemporal Economic Systems

  • W. A. Brock
  • A. Xepapadeas
  • A. N. Yannacopoulos


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.


Stochastic control Robust control Riccati equation Hot spot formation Pattern formation Hamilton-Jacobi Bellman equation Distance-dependent utility 

JEL Classification

C6 R12 Q26 



This research has been co-financed by the European Union (European Social Fund - ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF) - Research Funding Program: “Thalis - Athens University of Economics and Business - Optimal Management of Dynamical Systems of the Economy and the Environment: The Use of Complex Adaptive Systems”. W. Brock is grateful for financial and scientific support received from The Center for Robust Decision Making on Climate and Energy Policy (RDCEP) which is funded by a grant from the National Science Foundation (NSF) through the Decision Making Under Uncertainty (DMUU) program. He is also grateful to the Vilas Trust for financial support. None of the above is responsible for any errors, opinions, or shortcomings in this article. The authors are indebted to one of the anonymous referees whose thorough and critical reading of the manuscript and insightful comments highly contributed to the improvement of the current version of this work.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • W. A. Brock
    • 1
    • 2
  • A. Xepapadeas
    • 3
  • A. N. Yannacopoulos
    • 4
  1. 1.Department of EconomicsUniversity of WisconsinMadissonUSA
  2. 2.Department of EconomicsUniversity of MissouriColumbiaUSA
  3. 3.Department of International and European Economic StudiesAthens University of Economics and BusinessAthensGreece
  4. 4.Department of StatisticsAthens University of Economics and BusinessAthensGreece

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