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

Erwan Pierre, Stéphane Villeneuve and Xavier Warin
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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

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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

Keywords: investment; dividend policy; singular control; viscosity solution; nonlinear PDE (search for similar items in EconPapers)
Date: 2017-01
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Published in SIAM Journal on Financial Mathematics, 2017, 8 (1), pp.54 - 81. ⟨10.1137/16M1068323⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-01698641

DOI: 10.1137/16M1068323

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