Conditional and dynamic convex risk measures

We extend the definition of a convex risk measure to a conditional framework where additional information is available.We characterize these risk measures through the associated acceptance sets and prove a representation result in terms of conditional expectations.A suitable regularity property of conditional risk measures is defined and discussed. Finally, we introduce the concept of a dynamic convex risk measure as a family of successive conditional convex risk measures and characterize those satisfying some natural time consistency properties.As a reference example, illustrating all the proposed developments, we introduce a suitably defined dynamic version of the class of entropic risk measures