When dealing with integral terms which are generated in the process of functional derivation, one common point of the above reference is the use of Jensen's inequality
. Jensen's inequality
is simple and convenient, but it has a certain conservation.
Sababheh, "Improved Jensen's inequality
," Mathematical Inequalities & Applications, vol.
Then by using Jensen's Inequality
, we show that FUH cannot simultaneously hold true for both the sellers and buyers of the same forward currency contracts.
Secondly, by using Jensen's inequality
we obtain that
The proof is based on the multiplier method and makes use of some properties of convex functions including the use of the general Young's inequality and Jensen's inequality
. The paper is organized as follows.
Torres, "Diamond-a Jensen's inequality
on time scales," Journal of Inequalities and Applications, vol.
Based on combination of Leibniz-Newton formula, free-weighting matrices, Cauchy's inequality, modified version of Jensen's inequality
, decomposition technique of coefficient matrix, the use of suitable parameter-dependent Lyapunov-Krasovskii functional, model transformation, and linear matrix inequality technique, new delay-dependent robust exponential stability criteria for these systems will be obtained in terms of LMIs.
From Jensen's inequality
and inequality (11) we get:
However, this can be difficult, so we will upper bound this by using the Jensen's inequality
and a numerical method.
By Proposition 1, (1.2) and Jensen's inequality
The three are variants of Jensen's inequality
. The first inequality is a comparison of the expected value of a ratio to the ratio of the expected value, a problem that arises in pricing foreign exchange rates.
When the risk-free rate is time varying, Jensen's inequality
implies that the expected value of the conditional alpha in the beta pricing model is not the unconditional alpha.