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A solvable two-dimensional singular stochastic control problem with non convex costs

Author

Listed:
  • de Angelis, Tiziano

    (Center for Mathematical Economics, Bielefeld University)

  • Ferrari, Giorgio

    (Center for Mathematical Economics, Bielefeld University)

  • Moriarty, John

    (Center for Mathematical Economics, Bielefeld University)

Abstract

In this paper we provide a complete theoretical analysis of a two-dimensional degenerate non convex singular stochastic control problem. The optimisation is motivated by a storage-consumption model in an electricity market, and features a stochastic real-valued spot price modelled by Brownian motion. We find analytical expressions for the value function, the optimal control and the boundaries of the action and inaction regions. The optimal policy is characterised in terms of two monotone and discontinuous repelling free boundaries, although part of one boundary is constant and the smooth fit condition holds there.

Suggested Citation

  • de Angelis, Tiziano & Ferrari, Giorgio & Moriarty, John, 2016. "A solvable two-dimensional singular stochastic control problem with non convex costs," Center for Mathematical Economics Working Papers 561, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:561
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    File URL: https://pub.uni-bielefeld.de/download/2904729/2904730
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    References listed on IDEAS

    as
    1. Tiziano De Angelis & Giorgio Ferrari & John Moriarty, 2014. "A Non Convex Singular Stochastic Control Problem and its Related Optimal Stopping Boundaries," Papers 1405.2442, arXiv.org, revised Nov 2014.
    2. Dayanik, Savas & Karatzas, Ioannis, 2003. "On the optimal stopping problem for one-dimensional diffusions," Stochastic Processes and their Applications, Elsevier, vol. 107(2), pages 173-212, October.
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