International Journal of Advance Research Publication and Reviews

International Journal of Advance Research Publication and Reviews
Peer-Reviewed | Multi-Disciplinary Journal

ISSN: 3049-0103 (O)

Impact Factor: 4.33

The Mathematics of Borrowing Wisely: How Governments Optimise Debt

Author

Devagya Suresh Shukla

Abstract

 Government debt is usually discussed as a number to be minimised, but a growing body of mathematical and economic research instead treats it as a variable to be optimised: a quantity managed against explicit trade-offs between borrowing cost, financing risk, and economic growth. This review draws together three distinct strands of that research: debt sustainability analysis, as used by the International Monetary Fund (IMF); stochastic optimal control theory, as applied by mathematicians studying debt-reduction policy; and portfolio-based debt management, as practised by sovereign debt offices such as the United Kingdom’s Debt Management Office (DMO). It explains the mathematics underlying each approach and then examines a well-documented case, the 2010 Reinhart-Rogoff debt-threshold controversy, to show where such models can mislead policy if their assumptions are not scrutinised. The review concludes that mathematical optimisation does not identify a single “correct” debt level for a government, but provides a disciplined framework for making trade-offs between cost, risk, and uncertainty explicit. Given that the IMF projects global public debt to exceed 100 per cent of world GDP by 2029, understanding these frameworks has direct relevance to current fiscal policy debates worldwide.

Keywords

Sovereign Debt Optimization, • Public Finance Mathematics, Government Borrowing Strategy, Stochastic Calculus in Finance, • Yield Curve Modeling

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References

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