部分经济增长观测下的国债最优削减
Optimal Reduction of Public Debt under Partial Observation of the Economic Growth
摘要：
我们考虑一个旨在降低债务与国内生产总值（GDP）比率的政府。政府观察债务与GDP比率的水平，这是经济状况的一个指标，但不直接观察基本宏观经济条件的发展。政府的标准是最小化持有债务和债务削减政策的总预期成本之和。我们将此问题建模为部分观测下的奇异随机控制问题。该文件的贡献是双重的。首先，我们提供了一个一般公式的模型中，债务与国内生产总值的比率和宏观经济指标的值分别演变为扩散和跳跃扩散，系数取决于经济制度。这些都是通过一个有限状态的连续时间马尔可夫链。通过过滤技术，我们减少了原来的问题，一个等价的一个与充分的信息（所谓的分离问题），我们提供了一个一般的验证结果，在相关的最优停止问题充分的信息。其次，我们专门研究一个案例，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力学。在这种情况下，我们提供了最优的债务削减政策。这是在一个辅助的全二维最优停止问题中产生的连续自由边界。
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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