Jump to ContentJump to Main Navigation

The B.E. Journal of Theoretical Economics

Editor-in-Chief: Schipper, Burkhard

Ed. by Cervellati, Matteo / Fong, Yuk-fai / Peeters, Ronald / Puzzello , Daniela / Rivas, Javier

2 Issues per year

IMPACT FACTOR increased in 2014: 0.300

SCImago Journal Rank (SJR) 2014: 0.581
Source Normalized Impact per Paper (SNIP) 2014: 0.516
Impact per Publication (IPP) 2014: 0.387

Mathematical Citation Quotient (MCQ) 2014: 0.08

Geometric Asymptotic Approximation of Value Functions

Axel Anderson1

1Georgetown University,

Citation Information: The B.E. Journal of Theoretical Economics. Volume 9, Issue 1, ISSN (Online) 1935-1704, DOI: 10.2202/1935-1704.1532, December 2009

Publication History

Published Online:

This paper characterizes the behavior of value functions in dynamic stochastic discounted programming models near fixed points of the state space. When the second derivative of the flow payoff function is bounded, the value function is proportional to a linear function plus geometric term. A specific formula for the exponent of this geometric term is provided. This exponent continuously falls in the rate of patience.If the state variable is a martingale, the second derivative of the value function is unbounded. If the state variable is instead a strict local submartingale, then the same holds for the first derivative of the value function. Thus, the proposed approximation is more accurate than Taylor series approximation.The approximation result is used to characterize locally optimal policies in several fundamental economic problems.

Keywords: stochastic dynamic programming; value function approximation; learning

Comments (0)

Please log in or register to comment.