2022/07/05 by Daniel J. Fresen, Fresen, Daniel J.
Decision Sciences · Economics, Econometrics and Finance · #60E05 #60E15 #Economic theories and models #FOS: Mathematics #Probability (math.PR) #Risk and Portfolio Optimization
paper · pdf · doi:10.48550/arxiv.2207.01872
openalex publication_date 2022/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Following results of Kemperman and Pinelis, we show that if X and Y are real valued random variables such that 𝔼\vert Y\vert<∞ and for all non-decreasing convex φ:ℝ→ [0,∞), 𝔼φ(X)≤𝔼φ(Y), then for all s∈ℝ with ℙ\Y>s\≠ 0, ℙ\X≥𝔼(Y:Y>s)\≤ℙ\Y>s\. This bound is sharp in essentially the strictest possible sense: for any such Y and s there exists such an X with ℙ\X≥ 𝔼(Y:Y>s)\=ℙ\Y>s\.