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New Jensen-type inequalities and their applications

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  • Bar Light

Abstract

Convex analysis is fundamental to proving inequalities that have a wide variety of applications in economics and mathematics. In this paper we provide Jensen-type inequalities for functions that are, intuitively, "very" convex. These inequalities are simple to apply and can be used to generalize and extend previous results or to derive new results. We apply our inequalities to quantify the notion "more risk averse" provided in \cite{pratt1978risk}. We also apply our results in other applications from different fields, including risk measures, Poisson approximation, moment generating functions, log-likelihood functions, and Hermite-Hadamard type inequalities.

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  • Bar Light, 2020. "New Jensen-type inequalities and their applications," Papers 2007.09258, arXiv.org, revised Aug 2021.
    • Handle: RePEc:arx:papers:2007.09258
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    References listed on IDEAS

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    1. Light, Bar & Perlroth, Andres, 2021. "The Family of Alpha,[a,b] Stochastic Orders: Risk vs. Expected Value," Journal of Mathematical Economics, Elsevier, vol. 96(C).
    2. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    3. Menezes, C & Geiss, C & Tressler, J, 1980. "Increasing Downside Risk," American Economic Review, American Economic Association, vol. 70(5), pages 921-932, December.
    4. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
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