2020/07/17 by Bar Light, Light, Bar
Mathematics · #FOS: Economics and business #FOS: Mathematics #Functional Equations Stability Results #Mathematical Inequalities and Applications #Mathematical functions and polynomials #Optimization and Control (math.OC) #Probability (math.PR) #Theoretical Economics (econ.TH)
paper · pdf · doi:10.48550/arxiv.2007.09258
openalex publication_date 2020/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \citepratt1978risk. 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.