Ozan Hür | Searcharxiv

arXiv2025

Robust Stochastic Outperformance under Kullback-Leibler Ambiguity

We study the worst-case probability that $Y$ outperforms a benchmark $X$ when the law of $Y$ lies in a Kullback-Leibler neighbourhood of the benchmark. The max-min problem over couplings admits a tractable dual (via optimal transport), whose optimiser is an exponential tilt of the benchmark law. The resulting solution reduces to a one-parameter family indexed by regulizer $λ$, which controls the KL information budget and induces an increasing transfer of probability mass from lower to higher outcomes. The formulation can be evaluated from the baseline distribution and may serve as a distribution-wide scenario generation environment as well as a basis for robust performance assessment. Keywords: exponential tilting; optimal transport; stochastic dominance; stress testing.

math.PR↗

arXiv2025

Generalized Families of Fractional Stochastic Dominance

Introduced by Müller et al. in their seminal paper \cite{muller}, fractional stochastic dominance (SD) offers a nuanced approach to ordering distributions. In this paper, we propose a fundamentally new framework by replacing the fixed parameter $γ\in [0,1]$ in fractional SD with a function $\boldsymbolγ: \mathbb{R} \to [0,1]$. This yields two novel families, multi-fractional stochastic dominance (MFSD) and functional fractional stochastic dominance (FFSD). They enable the ranking of a broader range of distributions and incorporate a more informative utility class, including those with local non-concavities whose steepness varies depending on the location. Furthermore, our framework introduces the concept of partial greediness, which dynamically captures how behaviour of decision makers adapts to changes in wealth. We also extend this framework to encompass almost stochastic dominance. We provide the mathematical foundations of our generalized framework and study how it offers a novel tool for ordering distributions across various settings.

q-fin.MF↗