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On a Class of Infinite-Dimensional Singular Stochastic Control Problems

Author

Listed:
  • Federico, Salvatore

    (Center for Mathematical Economics, Bielefeld University)

  • Ferrari, Giorgio

    (Center for Mathematical Economics, Bielefeld University)

  • Riedel, Frank

    (Center for Mathematical Economics, Bielefeld University)

  • Röckner, Michael

    (Center for Mathematical Economics, Bielefeld University)

Abstract

We study a class of infinite-dimensional singular stochastic control problems with applications in economic theory and finance. The control process linearly affects an abstract evolution equation on a suitable partially-ordered infinite-dimensional space X, it takes values in the positive cone of X, and it has right-continuous and nondecreasing paths. We first provide a rigorous formulation of the problem by properly defining the controlled dynamics and integrals with respect to the control process. We then exploit the concave structure of our problem and derive necessary and sufficient first-order conditions for optimality. The latter are finally exploited in a specification of the model where we find an explicit expression of the optimal control. The techniques used are those of semigroup theory, vector-valued integration, convex analysis, and general theory of stochastic processes.

Suggested Citation

  • Federico, Salvatore & Ferrari, Giorgio & Riedel, Frank & Röckner, Michael, 2019. "On a Class of Infinite-Dimensional Singular Stochastic Control Problems," Center for Mathematical Economics Working Papers 614, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:614
    as

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    File URL: https://pub.uni-bielefeld.de/download/2935374/2935375
    File Function: First Version, 2019
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