Cash sub-additive risk statistics for portfolios.

The portfolios are a critical factor not only in risk analysis, but also in insurance and financial applications. In this paper, we consider a special class of risk statistics from the perspective of time value of the money. This new risk statistic can be uesd for the quantification of portfolio risk. By further developing the properties related to cash sub-additive risk statistics, we are able to derive representation results for such risk.