Before revision:  As to applications, we show how this multidimensional approach can be applied to measure the insolvency risk of a firm with interacted subsidiaries \protect .
After revision:  As to applications, we show how this multidimensional approach can be applied to measure the insolvency risk of a firm with interacted subsidiaries \protect\gamma -tolerant g-risk measures is investigated. Insurance g-risk measure and other ways to induce g-risk measures are also studied at the end of the paper .