论文标题
新的詹森型不平等及其应用
New Jensen-type inequalities and their applications
论文作者
论文摘要
凸分析对于证明在经济学和数学中应用各种应用的不平等至关重要。在本文中，我们提供了詹森型的不平等，以直观地“非常”凸。这些不等式易于应用，可用于概括和扩展先前的结果或得出新的结果。我们运用不平等来量化\ cite {pratt1978risk}中提供的“更多风险避开”概念。我们还将结果应用于来自不同领域的其他应用，包括风险度量，泊松近似，力矩生成功能，对数可能性功能和Hermite-Hadamard型不等式。
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.
