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Aspects concerning entropy and utility

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Abstract

Expected utility maximization problem is one of the most useful tools in mathematical finance, decision analysis and economics. Motivated by statistical model selection, via the principle of expected utility maximization, Friedman and Sandow (J Mach Learn Res 4:257–291, 2003a) considered the model performance question from the point of view of an investor who evaluates models based on the performance of the optimal strategies that the models suggest. They interpreted their performance measures in information theoretic terms and provided new generalizations of Shannon entropy and Kullback–Leibler relative entropy and called them U-entropy and U-relative entropy. In this article, a utility-based criterion for independence of two random variables is defined. Then, Markov’s inequality for probabilities is extended from the U-entropy viewpoint. Moreover, a lower bound for the U-relative entropy is obtained. Finally, a link between conditional U-entropy and conditional Renyi entropy is derived.

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Authors and Affiliations

  1. Department of Statistics, Science and Research Branch, Islamic Azad University, Tehran, Iran

    A. R. Hoseinzadeh

  2. Department of Statistics, Ferdowsi University of Mashhad, Mashhad, Iran

    G. R. Mohtashami Borzadaran

  3. Iran University of Science and Technology, Tehran, Iran

    G. H. Yari

Authors
  1. A. R. Hoseinzadeh
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  2. G. R. Mohtashami Borzadaran
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  3. G. H. Yari
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Corresponding author

Correspondence to G. R. Mohtashami Borzadaran.

Additional information

G. R. Mohtashami Borzadaran is a member of Ordered and Spatial Data Center of Excellence of Ferdowsi University of Mashhad, Iran.

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Hoseinzadeh, A.R., Mohtashami Borzadaran, G.R. & Yari, G.H. Aspects concerning entropy and utility. Theory Decis 72, 273–285 (2012). https://doi.org/10.1007/s11238-010-9232-5

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