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Envelope Condition Method with an Application to Default Risk Models

Cristina Arellano, Lilia Maliar, Serguei Maliar, Viktor Tsyrennikov
2014 Social Science Research Network  
JEL classification: C6 C61 C63 C68 Keywords: Dynamic programming Bellman equation Endogenous grid Curse of dimensionality Large scale Default risk a b s t r a c t We develop an envelope condition method (ECM) for dynamic programming problemsa 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
more » ... impler 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.
doi:10.2139/ssrn.2470009 fatcat:qpw7esg2gjgwthjccjz5nilydu