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Liquidity Management with Decreasing-returns-to-scale and Secured Credit Line

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

Abstract

This paper examines the dividend and investment policies of a cash constrained firm that has access to costly external funding. We depart from the literature by allowing the firm to issue collateralized debt to increase its investment in productive assets resulting in a performance sensitive interest rate on debt. We formulate this problem as a bi-dimensional singular control problem and use both a viscosity solution approch and a verification tech- nique to get qualitative properties of the value function. We further solve quasi-explicitly the control problem in two special cases.

Suggested Citation

  • Pierre, Erwan & Villeneuve, Stéphane & Warin, Xavier, 2014. "Liquidity Management with Decreasing-returns-to-scale and Secured Credit Line," TSE Working Papers 14-542, Toulouse School of Economics (TSE), revised Jun 2016.
    • Handle: RePEc:tse:wpaper:28789
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    References listed on IDEAS

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    3. 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.
    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. Black, Fischer & Cox, John C, 1976. "Valuing Corporate Securities: Some Effects of Bond Indenture Provisions," Journal of Finance, American Finance Association, vol. 31(2), pages 351-367, May.
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    8. 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.
    9. 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.
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    Citations

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    Cited by:

    1. Salvatore Federico & Giorgio Ferrari & Patrick Schuhmann, 2019. "A Model for the Optimal Management of Inflation," Department of Economics University of Siena 812, Department of Economics, University of Siena.
    2. Gaïgi, M’hamed & Ly Vath, Vathana & Scotti, Simone, 2022. "Optimal harvesting under marine reserves and uncertain environment," European Journal of Operational Research, Elsevier, vol. 301(3), pages 1181-1194.
    3. Etienne Chevalier & Vathana Ly Vath & Alexandre Roch, 2020. "Optimal Dividend and Capital Structure with Debt Covenants," Journal of Optimization Theory and Applications, Springer, vol. 187(2), pages 535-565, November.

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    More about this item

    Keywords

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

    JEL classification:

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

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