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Valuing programs with deterministic and stochastic cycles

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  • Paarsch, Harry J.
  • Rust, John

Abstract

In many dynamic programming problems, a mix of state variables exists - some exhibiting stochastic cycles and others having deterministic cycles. We derive a formula for the value function in infinite-horizon, stationary, Markovian decision problems by exploiting a special partitioned-circulant structure of the transition matrix [Pi]. Our strategy for computing the left-inverse of the matrix [I-[beta][Pi]], which is central to implementing Howard's policy iteration algorithm, yields significant improvements in computation time and major reductions in memory required. When the deterministic cycle is of order n, our cyclic inversion algorithm yields an O(n2) speed-up relative to the usual policy iteration algorithm.

Suggested Citation

  • Paarsch, Harry J. & Rust, John, 2009. "Valuing programs with deterministic and stochastic cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 33(3), pages 614-623, March.
    • Handle: RePEc:eee:dyncon:v:33:y:2009:i:3:p:614-623
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    Citations

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    Cited by:

    1. McClelland John & Rust John, 2018. "Strategic Timing of Investment over the Business Cycle: Machine Replacement in the US Rental Industry," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 238(3-4), pages 295-351, July.
    2. Avery Haviv, 2020. "Technical Note—Cyclic Variables and Markov Decision Processes," Operations Research, INFORMS, vol. 68(4), pages 1231-1237, July.
    3. Robert L. Bray, 2019. "Markov Decision Processes with Exogenous Variables," Management Science, INFORMS, vol. 65(10), pages 4598-4606, October.

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