Envelope Condition Method with an Application to Default Risk Models

Cristina Arellano, Lilia Maliar, Serguei Maliar and Viktor Tsyrennikov

No 2014-04, BYU Macroeconomics and Computational Laboratory Working Paper Series from Brigham Young University, Department of Economics, BYU Macroeconomics and Computational Laboratory

Abstract: We develop an envelope condition method (ECM) for dynamic programming problems –a tractable alternative to expensive conventional value function iteration. ECM has two novel features: First, to reduce the cost, ECM replaces expensive backward iteration on Bellman equation with relatively cheap forward iteration on an envelope condition. Second, to increase the accuracy of solutions, ECM solves for derivatives of a value function jointly with a 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 upto 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, and we …nd it to be fast, accurate and reliable.

Keywords: Dynamic programming; Value function iteration; Bellman equation; Endogenous grid; Envelope condition; Curse of dimensionality; Large scale; Sovereign debt; Default risk (search for similar items in EconPapers)
JEL-codes: C6 C61 C63 C68 (search for similar items in EconPapers)
Pages: 44 pages
Date: 2014-07
New Economics Papers: this item is included in nep-ban, nep-dge, nep-ore and nep-rmg
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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https://docs.google.com/file/d/0B6KGaihAO5TJN0dZaVRFWjFSZ0U/edit First version, 2014 (application/pdf)

Related works:
Journal Article: Envelope condition method with an application to default risk models (2016)
Working Paper: Envelope Condition Method with an Application to Default Risk Models (2015)
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Persistent link: https://EconPapers.repec.org/RePEc:byu:byumcl:201404

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