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

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

2010-12-28

arxiv.org/abs/1012.5850v1

Mathematics

Probability

Scientific paper

We study dynamic risk measures in a very general framework enabling to model uncertainty and processes with jumps. We previously showed the existence of a canonical equivalence class of probability measures hidden behind a given set of probability measures possibly non dominated. Taking advantage of this result, we exhibit a dual representation that completely characterizes the dynamic risk measure. We prove continuity and characterize time consistency. Then, we prove regularity for all processes associated to time consistent convex dynamic risk measures. We also study factorization through time for sublinear risk measures. Finally we consider examples (uncertain volatility and G-expectations).

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