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摘要翻译：
我们认为一个政府的目标是降低一个国家的债务与国内生产总值(GDP)的比率。政府观察债务与国内生产总值比率的水平和经济状况的指标，但不直接观察基本宏观经济条件的发展。政府的标准是使持有债务和减少债务政策的总预期成本之和最小化。我们将此问题建模为部分观测下的奇异随机控制问题。论文的贡献是双重的。首先，我们给出了模型的一般表达式，其中债务与GDP比率的水平和宏观经济指标的值分别以扩散和跳跃扩散的形式演化，其系数依赖于经济体制。这些都是通过一个有限状态的连续时间马尔可夫链来描述的。通过过滤技术将原问题归结为一个完全信息下的等价问题（即所谓的分离问题），并给出了完全信息下相关最优停止问题的一般验证结果。其次，我们专门研究了一个案例，其中经济只面临两种制度，宏观经济指标具有适当的扩散动态。在此背景下，我们提出了最优的债务削减政策。这是由一个辅助的全二维最优停止问题产生的连续自由边界给出的。
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英文标题：
《Optimal Reduction of Public Debt under Partial Observation of the
Economic Growth》
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作者：
Giorgia Callegaro, Claudia Ceci, Giorgio Ferrari
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最新提交年份：
2019
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分类信息：
一级分类：Mathematics 数学
二级分类：Optimization and Control 优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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一级分类：Economics 经济学
二级分类：General Economics 一般经济学
分类描述：General methodological, applied, and empirical contributions to economics.
对经济学的一般方法、应用和经验贡献。
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一级分类：Quantitative Finance 数量金融学
二级分类：Economics 经济学
分类描述：q-fin.EC is an alias for econ.GN. Economics, including micro and macro economics, international economics, theory of the firm, labor economics, and other economic topics outside finance
q-fin.ec是econ.gn的别名。经济学，包括微观和宏观经济学、国际经济学、企业理论、劳动经济学和其他金融以外的经济专题
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英文摘要：
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 minimize the sum of the total expected costs of holding debt and of debt's 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 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. These are described through a finite-state continuous-time Markov chain. We reduce via filtering techniques the original problem 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 specialize 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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PDF链接：
https://arxiv.org/pdf/1901.08356
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