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An extension of the usual model in statistical decision theory with applications to stochastic optimization problems

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  • Balder, E. J.

Abstract

By employing fundamental results from "geometric" functional analysis and the theory of multifunctions we formulate a general model for (nonsequential) statistical decision theory, which extends Wald's classical model. From central results that hold for the model we derive a general theorem on the existence of admissible nonrandomized Bayes rules. The generality of our model makes it also possible to apply these results to some stochastic optimization problems. In an appendix we deal with the question of sufficiency reduction.

Suggested Citation

  • Balder, E. J., 1980. "An extension of the usual model in statistical decision theory with applications to stochastic optimization problems," Journal of Multivariate Analysis, Elsevier, vol. 10(3), pages 385-397, September.
    • Handle: RePEc:eee:jmvana:v:10:y:1980:i:3:p:385-397
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    Cited by:

    1. Balbus, Łukasz & Reffett, Kevin & Woźny, Łukasz, 2012. "Stationary Markovian equilibrium in altruistic stochastic OLG models with limited commitment," Journal of Mathematical Economics, Elsevier, vol. 48(2), pages 115-132.
    2. Jaśkiewicz, Anna & Nowak, Andrzej S., 2014. "Stationary Markov perfect equilibria in risk sensitive stochastic overlapping generations models," Journal of Economic Theory, Elsevier, vol. 151(C), pages 411-447.
    3. A. S. Nowak, 2010. "On a Noncooperative Stochastic Game Played by Internally Cooperating Generations," Journal of Optimization Theory and Applications, Springer, vol. 144(1), pages 88-106, January.

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