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Explicit formula for the optimal government debt ceiling

Author

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  • Abel Cadenillas

    (University of Alberta)

  • Ricardo Huamán-Aguilar

    (University of Alberta)

Abstract

Motivated by the current debt crisis in the world, we develop a stochastic debt control model to study the optimal government debt ceiling, or equivalently the optimal ceiling for government debt. We consider a government that wants to control its debt by imposing an upper bound or ceiling on its debt-to-GDP ratio. We assume that debt generates a cost for the country, and this cost is an increasing and convex function of debt ratio. The government can intervene to reduce its debt ratio, but there is a cost generated by this reduction. The goal of the government is to find the optimal control that minimizes the expected total cost. We obtain an explicit solution for the government debt problem, that gives an explicit formula for optimal government debt ceiling. Moreover, we derive a rule for optimal debt policy in terms of the optimal government debt ceiling. In an extension of the model, we find that countries with a strong positive link between debt and economic growth should have a high optimal debt ceiling. This paper provides the first theoretical model for the optimal government debt ceiling.

Suggested Citation

  • Abel Cadenillas & Ricardo Huamán-Aguilar, 2016. "Explicit formula for the optimal government debt ceiling," Annals of Operations Research, Springer, vol. 247(2), pages 415-449, December.
    • Handle: RePEc:spr:annopr:v:247:y:2016:i:2:d:10.1007_s10479-015-2052-9
    DOI: 10.1007/s10479-015-2052-9
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    4. Abel Cadenillas & Ricardo Huamán-Aguilar, 2018. "On the Failure to Reach the Optimal Government Debt Ceiling," Risks, MDPI, vol. 6(4), pages 1-28, December.
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    6. Yoshioka, Hidekazu & Yaegashi, Yuta, 2019. "A finite difference scheme for variational inequalities arising in stochastic control problems with several singular control variables," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 156(C), pages 40-66.
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    9. Giorgio Ferrari & Tiziano Vargiolu, 2020. "On the singular control of exchange rates," Annals of Operations Research, Springer, vol. 292(2), pages 795-832, September.
    10. Callegaro, Giorgia & Ceci, Claudia & Ferrari, Giorgio, 2019. "Optimal Reduction of Public Debt under Partial Observation of the Economic Growth," Center for Mathematical Economics Working Papers 608, Center for Mathematical Economics, Bielefeld University.
    11. Dianetti, Jodi & Ferrari, Giorgio, 2019. "Nonzero-Sum Submodular Monotone-Follower Games. Existence and Approximation of Nash Equilibria," Center for Mathematical Economics Working Papers 605, Center for Mathematical Economics, Bielefeld University.
    12. Dammann, Felix & Rodosthenous, Néofytos & Villeneuve, Stéphane, 2024. "A Stochastic Non-Zero-Sum Game of Controlling the Debt-to-GDP Ratio," TSE Working Papers 24-1481, Toulouse School of Economics (TSE).
    13. Klaus Werner Schmidt & Öncü Hazır, 2019. "Formulation and solution of an optimal control problem for industrial project control," Annals of Operations Research, Springer, vol. 280(1), pages 337-350, September.
    14. Wei-han Liu, 2023. "Attaining stochastic optimal control over debt ratios in U.S. markets," Review of Quantitative Finance and Accounting, Springer, vol. 61(3), pages 967-993, October.
    15. Dammann, Felix & Rodosthenous, Néofytos & Villeneuve, Stéphane, 2023. "Debt management game and debt ceiling," TSE Working Papers 23-1430, Toulouse School of Economics (TSE).
    16. Barucci, Emilio & Brachetta, Matteo & Marazzina, Daniele, 2023. "On the feasibility of a debt redemption fund," Economic Modelling, Elsevier, vol. 119(C).
    17. Matteo Brachetta & Claudia Ceci, 2021. "A Stochastic Control Approach to Public Debt Management," Papers 2107.10491, arXiv.org.
    18. Jussi Lindgren, 2021. "Examination of Interest-Growth Differentials and the Risk of Sovereign Insolvency," Risks, MDPI, vol. 9(4), pages 1-14, April.
    19. Ferrari, Giorgio & Rodosthenous, Neofytos, 2018. "Optimal Management of Debt-To-GDP Ratio with Regime-Switching Interest Rate," Center for Mathematical Economics Working Papers 589, Center for Mathematical Economics, Bielefeld University.
    20. Giorgia Callegaro & Claudia Ceci & Giorgio Ferrari, 2020. "Optimal reduction of public debt under partial observation of the economic growth," Finance and Stochastics, Springer, vol. 24(4), pages 1083-1132, October.

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