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Numerical Approximation of a Cash-Constrained Firm Value with Investment Opportunities

Author

Listed:
  • Erwan Pierre
  • Stéphane Villeneuve

    (TSM - Toulouse School of Management Research - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - CNRS - Centre National de la Recherche Scientifique - TSM - Toulouse School of Management - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse)

  • Xavier Warin

    (EDF R&D - EDF R&D - EDF - EDF)

Abstract

We consider a singular control problem with regime switching that arises in problems of optimal investment decisions of cash-constrained firms. The value function is proved to be the unique viscosity solution of the associated Hamilton--Jacobi--Bellman equation. Moreover, we give regularity properties of the value function as well as a description of the shape of the control regions. Based on these theoretical results, a numerical deterministic approximation of the related HJB variational inequality is provided. We finally show that this numerical approximation converges to the value function. This allows us to describe the investment and dividend optimal policies

Suggested Citation

  • Erwan Pierre & Stéphane Villeneuve & Xavier Warin, 2017. "Numerical Approximation of a Cash-Constrained Firm Value with Investment Opportunities," Post-Print halshs-01698641, HAL.
  • Handle: RePEc:hal:journl:halshs-01698641
    DOI: 10.1137/16M1068323
    as

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