# Jensen's inequality

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## Jensen's inequality

[′jen·sənz ‚in·i′kwäl·ədē]
(mathematics)
A general inequality satisfied by a convex function where the xi are any numbers in the region where ƒ is convex and the ai are nonnegative numbers whose sum is equal to 1.
If a1, a2, …, an are positive numbers and s > t > 0, then (a1 s + a2 s + ⋯ + an s )1/ s is less than or equal to (a1 t + a2 t + ⋯ + an t )1/ t .
References in periodicals archive ?
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.
7) By using Jensen's Inequality, we show that forward rates cannot be expected to be unbiased estimators of corresponding future spot rates for both buyers and sellers of the same forward currency contracts.
Fourthly, we resort to neither Jensen's inequality with delay-dividing approach nor the free-weighting matrix method compared with previous results.
We use three inequalities in Lemma 7 combined with the quadratic convex combination implied by Lemma 6, rather than Jensen's inequality and the linear convex combination.
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.
Torres, "Diamond-a Jensen's inequality on time scales," Journal of Inequalities and Applications, vol.
However, this can be difficult, so we will upper bound this by using the Jensen's inequality and a numerical method.
The major conclusions is that Jensen's inequality is not a theoretical and superfluous exercise in finance as some have advocated.
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.
That the raw material would benefit from some purification in the convex region arises naturally from Jensen's inequality which states that for a P(x) function that is convex over [a, b], and for an arbitrary measure with mass density function f(x),
Using Jensen's Inequality, one can easily verify that a risk neutral firm prefers less price fluctuations if [[Gama.
For example, in chapter 1, Jensen's inequality is claimed to state E u(x) [is less than] E(x) (p.
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