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Logarithmic transformations for discrete-time, finite-horizon stochastic control problems

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Abstract

Using logarithmic transformations, we construct discrete-time stochastic control problems where the optimal value function (cost-to-go) belongs to a same parametrized class of functions that remains invariant under the dynamic programming operator. This extends a well-known property of the classical LQG problems, where the optimal value function is a quadratic. Some related questions are also discussed.

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Authors and Affiliations

  1. Dipartimento di Matematica Pura ed Applicata, Università di Padova, 35131, Padova, Italy

    Francesca Albertini & Wolfgang J. Runggaldier

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  1. Francesca Albertini
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  2. Wolfgang J. Runggaldier
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Albertini, F., Runggaldier, W.J. Logarithmic transformations for discrete-time, finite-horizon stochastic control problems. Appl Math Optim 18, 143–161 (1988). https://doi.org/10.1007/BF01443619

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  • DOI: https://doi.org/10.1007/BF01443619

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