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

Let (Ω,Σ) be a measurable space and let B(Σ) denote the Banach space of bounded, Σ-measurable functions on Ω equipped with the sup-norm. Ω is the set of states of nature and B(Σ) is the set of all (measurable) risks (see Artzner et al. [2]). A measure of risk is a mapping ρ : B(Σ) −→ R. Coherent risk measures were introduced in [5] (under the name of "upper expectations") and further studied in...

We discuss the quantification of financial risk in terms of monetary risk measures. Special emphasis is on dual representations of convex risk measures, relations to expected utility and other valuation concepts, conditioning, and consistency in discrete time.

Coherent and convex risk measures, Choquet expectation and Peng’s g-expectation are all generalizations of mathematical expectation. All have been widely used to assess financial riskiness under uncertainty. In this paper, we investigate differences amongst these risk measures and expectations. For this purpose, we constrain our attention of coherent and convex risk measures, and Choquet expect...

In this paper, we define several disclosure risk measures for microdata. We will analyze disclosure risk based on the disclosure control techniques applied to initial microdata. Disclosure Control is the discipline concerned with the modification of data containing confidential information about individual entities, such as persons, households, businesses, etc. in order to prevent third parties...