国债管理的随机控制方法
A Stochastic Control Approach to Public Debt Management
摘要：
讨论了一类随机环境下的债务管理问题。我们提出了一个债务与GDP比率模型，其中政府干预通过财政政策影响公共债务和GDP增长率的同时。我们允许随机利率和可能的相关性与GDP增长率通过依赖的过程（利率和GDP增长率）的随机因素，这可能代表任何相关的宏观经济变量，如经济状况。我们处理的问题是，政府的目标是确定财政政策，以尽量减少一般功能成本。证明了该价值函数是Hamilton-Jacobi-贝尔曼方程的粘性解，并给出了基于经典解的一个验证定理.我们调查的候选人的形式最佳财政政策在许多情况下的利益，提供有趣的政策见解。最后，我们讨论了两个应用的债务削减问题和债务平滑，提供明确的表达式的价值函数和最优政策在某些特殊情况下。
英文摘要：
We discuss a class of debt management problems in a stochastic environment model. We propose a model for the debt-to-GDP (Gross Domestic Product) ratio where the government interventions via fiscal policies affect the public debt and the GDP growth rate at the same time. We allow for stochastic interest rate and possible correlation with the GDP growth rate through the dependence of both the processes (interest rate and GDP growth rate) on a stochastic factor which may represent any relevant macroeconomic variable, such as the state of economy. We tackle the problem of a government whose goal is to determine the fiscal policy in order to minimize a general functional cost. We prove that the value function is a viscosity solution to the Hamilton-Jacobi-Bellman equation and provide a Verification Theorem based on classical solutions. We investigate the form of the candidate optimal fiscal policy in many cases of interest, providing interesting policy insights. Finally, we discuss two applications to the debt reduction problem and debt smoothing, providing explicit expressions of the value function and the optimal policy in some special cases.
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