On the Failure to Reach the Optimal Government Debt Ceiling

Cadenillas, Abel; Huamán-Aguilar, Ricardo

doi:10.3390/risks6040138

Cited by 12 publications

(28 citation statements)

References 28 publications

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“…We provide here some comments on our formulation of the optimal debt reduction problem. In line with the recent literature [8,9,31,32] on stochastic control models for debt management, the cost/loss function h appearing in the government's objective functional is nondecreasing and null when the debt level is zero. While the latter requirement can be made without loss of generality, the former implicitly means that the government believes that disadvantages arising from debt far outweigh the advantages, and therefore neglects any potential social and financial benefit arising from having debt (cf.…”

Section: Assumption 24 (I)supporting

confidence: 58%

“…Moreover, since ρ satisfies Assumption 4.3 and 0 ≤ π t ≤ 1 for any (x, y) ∈ O, one has that 9) and the family of random variables is a.s. continuous for any t ≥ 0, it is not hard to verify that (x, y) → J (x,y) (τ ) is continuous for any given τ ≥ 0. Hence v is upper semicontinuous.…”

Section: Formulation and Preliminary Resultsmentioning

confidence: 99%

“…Any decrease of the debt ratio results in proportional costs, and the government aims at choosing a debt-reduction policy that minimises the total expected loss of holding debt, plus the total expected costs of interventions on the debt ratio. In line with recent papers on stochastic control methods for optimal debt management (see Cadenillas and Huamán-Aguilar [8,9], Ferrari [31] and Ferrari and Rodosthenous [32]), we model the previous problem as a singular stochastic control problem. However, differently to all previous works, our problem is formulated in a partial observation setting, thus leading to a completely different mathematical analysis.…”

Section: Introductionmentioning

confidence: 99%

“…As already noticed above, our paper is placed among those recent works addressing the problem of optimal debt management via continuous-time stochastic control techniques. In particular, Cadenillas and Huamán-Aguilar [8,9] model an optimal debt reduction problem as a one-dimensional control problem with singular and bounded-velocity controls, respectively. In the work by Ferrari and Rodosthenous [32], the government is allowed to increase and decrease the current level of the debt ratio, and the interest rate on debt is modulated by a continuous-time observable Markov chain.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Optimal reduction of public debt under partial observation of the economic growth

2020

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We consider a government that aims at reducing the debt-to-(gross domestic product) (GDP) ratio of a country. The government observes the level of the debt-to-GDP ratio and an indicator of the state of the economy, but does not directly observe the development of the underlying macroeconomic conditions. The government’s criterion is to minimise the sum of the total expected costs of holding debt and of debt reduction policies. We model this problem as a singular stochastic control problem under partial observation. The contribution of the paper is twofold. Firstly, we provide a general formulation of the model in which the level of the debt-to-GDP ratio and the value of the macroeconomic indicator evolve as a diffusion and a jump-diffusion, respectively, with coefficients depending on the regimes of the economy. The latter are described through a finite-state continuous-time Markov chain. We reduce the original problem via filtering techniques to an equivalent one with full information (the so-called separated problem), and we provide a general verification result in terms of a related optimal stopping problem under full information. Secondly, we specialise to a case study in which the economy faces only two regimes and the macroeconomic indicator has a suitable diffusive dynamics. In this setting, we provide the optimal debt reduction policy. This is given in terms of the continuous free boundary arising in an auxiliary fully two-dimensional optimal stopping problem.

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Section: Assumption 24 (I)supporting

confidence: 58%

Section: Formulation and Preliminary Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Optimal reduction of public debt under partial observation of the economic growth

2020

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“…is the functional defined in (9). Let A x,α be the collection of all admissible controls with the initial data (x, α).…”

Section: Controlled Switching Diffusionsmentioning

confidence: 99%

A survey of numerical solutions for stochastic control problems: Some recent progress

Jin¹,

Qiu²,

Tran³

et al. 2022

NACO

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<p style='text-indent:20px;'>This paper presents a survey on some of the recent progress on numerical solutions for controlled switching diffusions. We begin by recalling the basics of switching diffusions and controlled switching diffusions. We then present regular controls and singular controls. The main objective of this paper is to provide a survey on some recent advances on Markov chain approximation methods for solving stochastic control problems numerically. A number of applications in insurance, mathematical biology, epidemiology, and economics are presented. Several numerical examples are provided for demonstration.</p>

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A Stochastic Non-zero-Sum Game of Controlling the Debt-to-GDP Ratio

Dammann,

Rodosthenous,

Villeneuve

2024

Appl Math Optim

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We introduce a non-zero-sum game between a government and a legislative body to study the optimal level of debt. Each player, with different time preferences, can intervene on the stochastic dynamics of the debt-to-GDP ratio via singular stochastic controls, in view of minimizing non-continuously differentiable running costs. We completely characterise Nash equilibria in the class of Skorokhod-reflection-type policies. We highlight the importance of different time preferences resulting in qualitatively different type of equilibria. In particular, we show that, while it is always optimal for the government to devise an appropriate debt issuance policy, the legislator should optimally impose a debt ceiling only under relatively low discount rates and a laissez-faire policy can be optimal for high values of the legislator’s discount rate.

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On the Failure to Reach the Optimal Government Debt Ceiling

Cited by 12 publications

References 28 publications

Optimal reduction of public debt under partial observation of the economic growth

Optimal reduction of public debt under partial observation of the economic growth

A survey of numerical solutions for stochastic control problems: Some recent progress

A Stochastic Non-zero-Sum Game of Controlling the Debt-to-GDP Ratio

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