Abstract
Abstract In this paper, we conducted a comprehensive examination of the Extended Gini Shortfall (EGS) as a flexible risk measure for portfolio selection, employing various approaches. The EGS measure possesses desirable properties, such as coherence, risk and variability measurement, and risk aversion. Additionally, we introduced the Reward Risk Ratio induced from EGS and explored its associated properties. Our main focus centered on a convex optimization problem, where the objective was to minimize portfolio risk while adhering to reward and budget constraints. We demonstrated the effectiveness of the obtained theoretical results through a practical application.
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