Jensen’s Inequality for g-Convex Function under g-Expectation
نویسندگان
چکیده
A real valued function defined on R is called g–convex if it satisfies the following “generalized Jensen’s inequality” under a given g-expectation, i.e., h(E[X ]) ≤ E[h(X)], for all random variables X such that both sides of the inequality are meaningful. In this paper we will give a necessary and sufficient conditions for a C-function being g-convex. We also studied some more general situations. We also studied g-concave and g-affine functions.
منابع مشابه
JENSEN’S INEQUALITY FOR GG-CONVEX FUNCTIONS
In this paper, we obtain Jensen’s inequality for GG-convex functions. Also, we get in- equalities alike to Hermite-Hadamard inequality for GG-convex functions. Some examples are given.
متن کاملRisk Measures and Nonlinear Expectations
Coherent and convex risk measures, Choquet expectation and Peng’s g-expectation are all generalizations of mathematical expectation. All have been widely used to assess financial riskiness under uncertainty. In this paper, we investigate differences amongst these risk measures and expectations. For this purpose, we constrain our attention of coherent and convex risk measures, and Choquet expect...
متن کاملOn a Converse of Jensen’s Discrete Inequality
There are many important inequalities which are particular cases of Jensen’s inequality among which are the weighted A − G − H inequality, Cauchy’s inequality, the Ky Fan and Hölder’s inequalities. One can see that the lower bound zero is of global nature since it does not depend on p, x but only on f and the interval I whereupon f is convex. We give in 1 an upper global bound i.e., depending o...
متن کاملJensen’s Operator Inequality for Strongly Convex Functions
We give a Jensen’s operator inequality for strongly convex functions. As a corollary, we improve Hölder-McCarthy inequality under suitable conditions. More precisely we show that if Sp (A) ⊂ I ⊆ (1,∞), then 〈Ax, x〉 r ≤ 〈Ax, x〉 − r − r 2 (
متن کاملProbability Theory
4 The Lebesgue integral and expectation 14 4.1 The Lebesgue integral and convergence theorems . . . . . . . . . . . . . . . . . . . . . . . . . 14 4.2 Probability measures and modes of convergence . . . . . . . . . . . . . . . . . . . . . . . . . . 20 4.3 Uniform integrability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.4 Jensen’s inequality . . . . . ...
متن کامل