arXiv Paper Released on Axiomatic Characterization of Jensen Gap Functionals

Lilian Hu and Ruodu Wang released the paper "Jensen gaps and the decomposition principle" on arXiv, providing an axiomatic characterization of Jensen gap functionals of the form ρ(X)=E[f(X)]-f(E[X]). Such functionals cover typical examples such as excess growth rate, utility premium, KL divergence, and variance, and are closely related to variability measures. The paper proves that on atomless probability spaces, law invariance combined with the binary decomposition principle is sufficient to characterize Jensen gaps for simple random variables. Under appropriate continuity conditions, this characterization extends to broader classes of random variables, such as compactly supported and integrable random variables, corresponding to the identification of logarithmic, x log x, power-type generators, as well as exponential and quadratic generators, respectively.

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