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Stochastic Optimal Control in Infinite Dimensions - Dynamic Programming and HJB Equations

Author

Listed:
  • Giorgio Fabbri

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

  • Fausto Gozzi

    (Dipartimento di Economia e Finanza [Roma] - LUISS - Libera Università Internazionale degli Studi Sociali Guido Carli [Roma])

  • Andrzej Swiech

    (School of Mathematics - Georgia Institute of Technology - Georgia Institute of Technology [Atlanta])

Abstract

Providing an introduction to stochastic optimal control in infinite dimensions, this book gives a complete account of the theory of second-order HJB equations in infinite-dimensional Hilbert spaces, focusing on its applicability to associated stochastic optimal control problems. It features a general introduction to optimal stochastic control, including basic results (e.g. the dynamic programming principle) with proofs, and provides examples of applications. A complete and up-to-date exposition of the existing theory of viscosity solutions and regular solutions of second-order HJB equations in Hilbert spaces is given, together with an extensive survey of other methods, with a full bibliography. In particular, Chapter 6, written by M. Fuhrman and G. Tessitore, surveys the theory of regular solutions of HJB equations arising in infinite-dimensional stochastic control, via BSDEs. The book will be of interest to both pure and applied researchers working in the control theory of stochastic PDEs, and in PDEs in infinite dimensions. Readers from other fields who want to learn the basic theory will also find it useful. The prerequisites are: standard functional analysis, the theory of semigroups of operators and its use in the study of PDEs, some knowledge of the dynamic programming approach to stochastic optimal control problems in finite dimensions, and the basics of stochastic analysis and stochastic equations in infinite-dimensional spaces.

Suggested Citation

  • Giorgio Fabbri & Fausto Gozzi & Andrzej Swiech, 2017. "Stochastic Optimal Control in Infinite Dimensions - Dynamic Programming and HJB Equations," Post-Print hal-01505767, HAL.
    • Handle: RePEc:hal:journl:hal-01505767
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