Control Theory Methods in Economics

Online-Ressource (IX, 258 p)

online resource

1 Introduction to Control Theory1.1 Transition from the calculus of variations to optimal control -- 1.2 Transition from theory to practice -- References -- 2 Continuous Time Models -- 2.0 Overview of control problems -- 2.1 Observability and controllability -- 2.2 Stability analysis -- 2.3 The maximum principle -- 2.4 Constraints -- 2.5 Example 1; A limit pricing model. -- 2.6 Example 2; reaching a steady state cycle -- References -- 3 Discrete Time Models -- 3.0 Introduction -- 3.1 General deterministic and discrete control problems -- 3.2 The linear quadratic problem -- 3.3 Analytic solution of the Riccati equation -- 3.4 Equivalent dynamic equations -- 3.5 Discrete control of nonlinear systems -- 3.6 Observability and observers -- 3.7 Economic examples -- References -- 4 Stochastic Control Theory -- 4.0 Introduction -- 4.1 Stochastic processes under control -- 4.2. Economic applications -- 4.3 Kalman filtering methods -- 4.4 Concluding remarks -- References -- 5 Economic Implications of Stochastic Control -- 5.0 Introduction -- 5.1 Time inconsistency problems -- 5.2 Short-run vs. long-run optimality -- 5.3 Model of adjustment costs with rational expectations -- 5.4 An application to new growth theory: dynamic adjustments with learning by doing -- 5.5 Concluding remarks. -- References -- 6 Variable Structure Systems -- 6.0 Introduction -- 6.1 The variable structure control formulation -- 6.2 A VSC approximation of an optimal control law -- 6.3 Example; The expectations-augmented Phillips relation -- 6.4 Concluding remarks -- References -- 7 Risk Sensitivity, Adjustment of Control and Estimation -- 7.0 Introduction -- 7.1 Learning process in differential games -- 7.2 Adjustment costs in portfolio models -- 7.3 Econometric estimation of controlled systems -- 7.4 Estimating transversality conditions -- 7.5 Concluding remarks -- References.

10.1007/978-1-4615-6285-6 [DOI]

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