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

Abstract

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).

References in corpus (4)

• Dual formulation of second order target problems
• Pricing, Hedging and Optimally Designing Derivatives Via Minimization of Risk Measures
• Random G-expectations
• Function spaces and capacity related to a Sublinear Expectation: application to G-Brownian Motion Pathes

Cited by in corpus (4)

• Coherent Price Systems and Uncertainty-Neutral Valuation
• Minimal supersolutions of BSDEs under volatility uncertainty
• A new probabilistic approach to non local and fully non linear second order partial differential equations
• Quasi-sure analysis, aggregation and dual representations of sublinear expectations in general spaces