Conditional and dynamic convex risk measures
- Cite this article as:
- Detlefsen, K. & Scandolo, G. Finance Stochast. (2005) 9: 539. doi:10.1007/s00780-005-0159-6
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.