Scandinavian Working Papers in Economics

Working Papers,
Copenhagen Business School, Department of Finance

No 2004-4: Upper Bounds on Numerical Approximation Errors

Peter Raahauge
Additional contact information
Peter Raahauge: Department of Finance, Copenhagen Business School, Postal: Department of Finance, Copenhagen Business School, Solbjerg Plads 3, A5, DK-2000 Frederiksberg, Denmark

Abstract: This paper suggests a method for determining rigorous upper bounds on approximation errors of numerical solutions to infinite horizon dynamic programming models. Bounds are provided for approximations of the value function and the policy function as well as the derivatives of the value function. The bounds apply to more general problems than existing bounding methods do. For instance, since strict concavity is not required, linear models and piecewise linear approximations can be dealt with. Despite the generality, the bounds perform well in comparison with existing methods even when applied to approximations of a standard(strictly concave)growth model.

Keywords: Numerical approximation errors; Bellman contractions; Error bounds

JEL-codes: G00

26 pages, June 21, 2006

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