Conditional Submodular Coherent Risk Measures

A family of conditional risk measures is introduced by considering a single period financial market, relying on a notion of conditioning for submodular capacities, which generalizes that introduced by Dempster. The resulting measures are expressed as discounted conditional Choquet expected values, take into account ambiguity towards uncertainty and allow for conditioning to “null” events. We also provide a characterisation of consistence of a partial assessment with a conditional submodular coherent risk measure. The latter amounts to test the solvability of a suitable sequence of linear systems