Abstract
In this paper, we establish a new coherent risk measure on Lp, which we refer to as the monotone mean Lp-deviation risk measure. Then, the related properties are discussed. Furthermore, from the perspective of acceptance set, we discuss the relationship between the monotone mean Lp-deviation risk measure and the monotone Sharpe ratio risk measure. Finally, we extend the monotone mean Lp-deviation risk measure to the multivariate setting.
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