Robust Control and Hot Spots in Spatiotemporal Economic Systems
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.
robust control pattern formation stochastic control riccati equation hot spot formation hamilton-jacobi bellman equation distance-dependent utility c6 r12 q26