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I am currently working to the numerical solution of a model similar to the consumption-savings decision model with hyperbolic discounting as in Krussel et al. (2003).

Even if hyperbolic discounting implies that the value function does not generally have the standard contraction property, some solutions to the problem have been implemented; for example Judd (2004) proposed perturbation methods from the exponential case and a local solution for small departures of hyperbolic discounting.

I have already implemented the basic model without hyperbolic discounting, using value function iterations on discretized policy grids.

Do you have suggestions for the extension to hyperbolic discounting? Is it possible to extend the basic model without moving to iterations in the Euler equation? Any advice or reference is welcomed.

Krusell, Per, and Anthony A. Smith Jr. "Consumption–savings decisions with quasi–geometric discounting." Econometrica 71.1 (2003): 365-375.

Judd, Kenneth L. "Existence, uniqueness, and computational theory for time consistent equilibria: A hyperbolic discounting example." (2004).

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Refer to Harris-Laibson 2001. They show the validity of the contraction mapping theorem in a neighborhood of the exponential consumption path.

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