Envelope Condition Method with an Application to Default Risk Models
Envelope Condition Method with an Application to Default Risk Models
复制标题
包络条件法及其在默认风险模型中的应用
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Viktor Tsyrennikov
中科院分区：
文献类型：
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作者：
C. Arellano;L. Maliar;Serguei Maliar;Viktor Tsyrennikov
我们开发了一个包络条件方法（ECM）的动态规划问题-一个易于处理的替代昂贵的传统值函数迭代（VFI）。ECM具有两个新特性：首先，为了减少Bellman方程的迭代成本，ECM使用包络条件构造策略函数，该包络条件比一阶条件更容易进行数值分析。第二，为了提高解的精度，ECM与值函数本身一起求解值函数的导数。我们补充ECM与其他计算技术，适用于高维问题，如基于模拟的网格，单项积分规则和无导数求解器。由此产生的值迭代ECM方法可以精确地求解至少多达20个状态变量的模型，并且可以成功地在精度和速度上与最先进的欧拉方程方法竞争。我们还使用ECM来解决一个具有挑战性的违约风险模型的价值和政策功能的扭结。
We develop an envelope condition method (ECM) for dynamic programming problems – a tractable alternative to expensive conventional value function iteration (VFI). ECM has two novel features: first, to reduce the cost of iteration on Bellman equation, ECM constructs policy functions using envelope conditions which are simpler to analyze numerically than first-order conditions. Second, to increase the accuracy of solutions, ECM solves for derivatives of value function jointly with value function itself. We complement ECM with other computational techniques that are suitable for high-dimensional problems, such as simulation-based grids, monomial integration rules and derivative-free solvers. The resulting value-iterative ECM method can accurately solve models with at least up to 20 state variables and can successfully compete in accuracy and speed with state-of-the-art Euler equation methods. We also use ECM to solve a challenging default risk model with a kink in value and policy functions.