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 by J. W. Pratt [Risk aversion in the small and in the large, in: Uncertainty in Economics, P. Diamond and M. Rothschild (eds.), Elsevier, Amsterdam (1978) 59–79]. 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.

Author information

Contact details are reproduced from the original publication and may be historical.

Bar Light

Graduate School of Business, Stanford University, Stanford, U.S.A.

barl@stanford.edu

Keywords

  • Convexity
  • (p
  • a
  • b)-convex functions
  • risk aversion
  • risk measures
  • moment generating functions
  • log-likelihood functions

Mathematics Subject Classification

26A51

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Suggested citation

B. Light. “New Jensen-Type Inequalities and their Applications.” Journal of Convex Analysis 29 (2022), No. 2, 605–622. https://doi.org/10.68381/jca29035

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Published by Heldermann Verlag, 2022. Rights now held by Banach Press LLC.