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We investigate a class of fractional distributionally robust optimization problems with uncertain probabilities. They consist in the maximization of ambiguous fractional functions representing reward-risk ratios and have a semi-infinite programming epigraphic formulation. We derive a new fully parameterized closed-form to compute a new bound on the size of the Wasserstein ambiguity ball. We design a data-driven reformulation and solution framework. The reformulation phase involves the derivation of the support function of the ambiguity set and the concave conjugate of the ratio function. We design modular bisection algorithms which enjoy the finite convergence property. This class of problems has wide applicability in finance, and we specify new ambiguous portfolio optimization models for the Sharpe and Omega ratios. The computational study shows the applicability and scalability of the framework to solve quickly large, industry-relevant-size problems, which cannot be solved in one day with state-of-the-art mixed-integer nonlinear programming (MINLP) solvers.

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This study investigates the mediating effect of brand experience on the relationship between customer motivation and engagement behavior and conceptualizes customer motivation from the multiple dimensions of information seeking, entertainment, and social interaction. Based on 565 valid questionnaires, it analyzes the impact of customer motivation on brand experience and customer engagement behavior using SPSS and AMOS. First, customer motivation with information seeking, entertainment, and social interaction significantly impacts customer brand experience. Second, customer brand experience significantly impacts customer engagement behavior of reuse, feedback, and WOM intentions. Finally, this study explores the mediating role of customer brand experience between customer motivation and customer engagement behavior and its impact on social media. It provides a reference for social media literature research. These findings will provide insights on motivating customers to participate in social media.