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We study dynamic risk measures in a very general framework enabling to modeluncertainty and processes with jumps. We previously showed the existence of acanonical equivalence class of probability measures hidden behind a given setof probability measures possibly non dominated. Taking advantage of thisresult, we exhibit a dual representation that completely characterizes thedynamic risk measure. We prove continuity and characterize time consistency.Then, we prove regularity for all processes associated to time consistentconvex dynamic risk measures. We also study factorization through time forsublinear risk measures. Finally we consider examples (uncertain volatility andG-expectations).

Dynamic risk measuring under model uncertainty: taking advantage of the hidden probability measure