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. © Springer-Verlag 2005.
CITATION STYLE
Detlefsen, K., & Scandolo, G. (2005). Conditional and dynamic convex risk measures. Finance and Stochastics, 9(4), 539–561. https://doi.org/10.1007/s00780-005-0159-6
Mendeley helps you to discover research relevant for your work.