The design of feedback rules in linear stochastic rational expectations models |
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| Affiliation: | 1. Gustave Roussy, Université Paris-Saclay, Imaging Department, Villejuif, and IR4M, Centre National de la Recherche Scientifique, Université Paris-Sud, Université Paris-Saclay, Villejuif;2. Imaging Department, Institut Bergonié, Bordeaux;3. Radiology Department, Assistance Publique-Hôpitaux de Paris, Hôpital Beaujon, Clichy;4. Radiology Department, Centre François Baclesse, Caen;5. Radiology Department, Centre Léon Bérard, Lyon;6. Radiology Department, Centre Oscar Lambret, Lille;7. Radiodiagnostics Department, Centre Claudius Regaud, Toulouse;8. Imaging Department, Institut Paoli Calmettes, Marseille;9. Radiodiagnostics Department, Centre René Gauducheau, ICO Nantes;10. Department of Abdominal and Digestive Imaging, Hôpital Saint-Eloi, Montpellier and Department of Radiology, McGill University Health Center, Montreal, Canada;11. Radiology Department, CHU La Pitié-Salpêtrière, Paris;12. Radiodiagnostics Department, Centre Jean Perrin, Clermont-Ferrand;13. Radiology Department, CHU Bicêtre, Le Kremlin-Bicêtre;14. Radiodiagnostics and Imaging Department, Institut Jean Godinot, Reims;15. Radiology Department, Hôpital Ambroise Paré, Boulogne-Billancourt;16. Radiology Department, CHU Hôtel-Dieu, Lyon;17. Radiology Department, CHU Henri Mondor, Créteil;18. Radiology Department, Centre Georges-François Leclerc, Dijon;19. Radiology Department, Hôpital Cochin, Paris;20. Service biostatistique et épidémiologie, Gustave Roussy and CESP Centre for Research in Epidemiology and Population Health, INSERM U1018, Paris-Sud Univ., Villejuif, France;1. Institut des sciences de la mer, University du Québec à Rimouski, Canada;2. Canada Research Chair on the Geochemistry of Coastal Hydrogeosystems, Département de biologie, chimie et géographie, Université du Québec à Rimouski, Canada;3. Takuvik Joint International Laboratory (UMI 3376), Université Laval, Canada;4. College of Chemistry and Chemical Engineering, Ocean University of China, China;5. Centre National de la Recherche Scientifique, France |
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| Abstract: | This paper is concerned with optimal and sub-optimal feedback rules for linear stochastic continuous time models with rational expectations. We consider four types of feedback rules: (1) the optimal but time-inconsistent rule which is available if the controller is able to commit himself or herself; (2) quasi-optimal and time-inconsistent rules of the form w = Dy where w is the vector of instruments, y the state vector and D a matrix of constants possibly with constraints; (3) the optimal time-consistent rule which is also linear in y; (4) ‘over-stable’ rules which have ‘too many’ stable roots. We show that rules of type (1) can be expressed and implemented as a form of integral control, all except type (2) satisfy certainty equivalence and that rules of type (4) will always be inferior to the optimal rule (1). These results are demonstrated in two illustrative examples. |
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