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In this paper, we develop some stochastic dominance
theorems for the location and scale family and linear combinations of
random variables and for risk lovers as well as risk averters that
extend results in Hadar and Russell (1971) and Tesfatsion (1976). The
results are discussed and applied to decision-making.
We show that Grüss-type probabilistic inequalities for covariances can be considerably sharpened when the underlying random variables are quadrant dependent in expectation (QDE). The herein established covariance bounds not only sharpen the classical Grüss inequality but also improve upon recently derived Grüss-type bounds under the assumption of quadrant dependency (QD), which is stronger than QDE. We illustrate our general results with examples based on specially devised bivariate distributions...
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