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Numerical approximation of a cash-constrained firm value with investment opportunities

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Listed:
  • Pierre, Erwan
  • Villeneuve, Stéphane
  • Warin, Xavier

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

  • Pierre, Erwan & Villeneuve, Stéphane & Warin, Xavier, 2016. "Numerical approximation of a cash-constrained firm value with investment opportunities," TSE Working Papers 16-637, Toulouse School of Economics (TSE).
    • Handle: RePEc:tse:wpaper:30394
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    References listed on IDEAS

    as
    1. Patrick Bolton & Hui Chen & Neng Wang, 2011. "A Unified Theory of Tobin's q, Corporate Investment, Financing, and Risk Management," Journal of Finance, American Finance Association, vol. 66(5), pages 1545-1578, October.
    2. Jean‐Paul Décamps & Thomas Mariotti & Jean‐Charles Rochet & Stéphane Villeneuve, 2011. "Free Cash Flow, Issuance Costs, and Stock Prices," Journal of Finance, American Finance Association, vol. 66(5), pages 1501-1544, October.
    3. Sunil Kumar & Kumar Muthuraman, 2004. "A Numerical Method for Solving Singular Stochastic Control Problems," Operations Research, INFORMS, vol. 52(4), pages 563-582, August.
    4. Bjarne Højgaard & Søren Asmussen & Michael Taksar, 2000. "Optimal risk control and dividend distribution policies. Example of excess-of loss reinsurance for an insurance corporation," Finance and Stochastics, Springer, vol. 4(3), pages 299-324.
    5. Julien Hugonnier & Semyon Malamud & Erwan Morellec, 2015. "Capital Supply Uncertainty, Cash Holdings, and Investment," The Review of Financial Studies, Society for Financial Studies, vol. 28(2), pages 391-445.
    6. Merton H. Miller & Franco Modigliani, 1961. "Dividend Policy, Growth, and the Valuation of Shares," The Journal of Business, University of Chicago Press, vol. 34, pages 411-411.
    7. Bjarne Hø Jgaard & Michael Taksar, 1999. "Controlling Risk Exposure and Dividends Payout Schemes:Insurance Company Example," Mathematical Finance, Wiley Blackwell, vol. 9(2), pages 153-182, April.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Investment; dividend policy; singular control; viscosity solution; nonlinear PDE;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • G35 - Financial Economics - - Corporate Finance and Governance - - - Payout Policy

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