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On continuity of state-dependent utilities

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  • Edoardo Berton
  • Alessandro Doldi
  • Marco Maggis

Abstract

State-dependent preferences for a general Savage's state space were shown in Wakker and Zank (1999) to admit a numerical representation in the form of the integral of a state-dependent utility, as soon as pointwise continuity of the preference ordering is assumed. In this paper we prove that such a state-dependent function inherits pointwise continuity from the preference ordering, providing in this way a positive answer to a conjecture posed in the aforementioned seminal work. We further apply this result to obtain an explicit representation of conditional Chisini means in the form of a conditional certainty equivalent.

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  • Edoardo Berton & Alessandro Doldi & Marco Maggis, 2024. "On continuity of state-dependent utilities," Papers 2401.09054, arXiv.org.
    • Handle: RePEc:arx:papers:2401.09054
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    References listed on IDEAS

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    1. Castagnoli, Erio & LiCalzi, Marco, 2006. "Benchmarking real-valued acts," Games and Economic Behavior, Elsevier, vol. 57(2), pages 236-253, November.
    2. Stanca, Lorenzo, 2020. "A simplified approach to subjective expected utility," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 151-160.
    3. Marco Frittelli & Marco Maggis, 2011. "Conditional Certainty Equivalent," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 41-59.
    4. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, September.
    5. Peter P. Wakker & Horst Zank, 1999. "State Dependent Expected Utility for Savage's State Space," Mathematics of Operations Research, INFORMS, vol. 24(1), pages 8-34, February.
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