Dynamic Games and Applications

, Volume 4, Issue 3, pp 257–289

Robust Control and Hot Spots in Spatiotemporal Economic Systems

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

DOI: 10.1007/s13235-014-0109-z

Cite this article as:
Brock, W.A., Xepapadeas, A. & Yannacopoulos, A.N. Dyn Games Appl (2014) 4: 257. doi:10.1007/s13235-014-0109-z


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 

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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