Monotone Mean <i>L^p</i>-Deviation Risk Measures

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.

Keywords

• coherent risk measure
• monotone Sharpe ratio
• mean standard deviation risk measure
• portfolio