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Envelope Condition Method with an Application to Default Risk Models

Viktor Tsyrennikov (), Serguei Maliar, Lilia Maliar and Cristina Arellano

No 1239, 2015 Meeting Papers from Society for Economic Dynamics

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 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, and we find it to be fast, accurate and reliable.

Date: 2015
New Economics Papers: this item is included in nep-ban, nep-cmp, nep-dge and nep-rmg
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Related works:
Journal Article: Envelope condition method with an application to default risk models (2016) Downloads
Working Paper: Envelope Condition Method with an Application to Default Risk Models (2014) Downloads
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