Abstract
Time consistency is a crucial property for dynamic risk measures. Making use of the dual representation for conditional risk measures, we characterize the time consistency by a cocycle condition for the minimal penalty function.
Taking advantage of this cocycle condition, we introduce a new methodology for the construction of time-consistent dynamic risk measures. Starting with BMO martingales, we provide new classes of time-consistent dynamic risk measures. These families generalize those obtained from backward stochastic differential equations. Quite importantly, starting with right-continuous BMO martingales, this construction naturally leads to paths with jumps.
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Bion-Nadal, J. Dynamic risk measures: Time consistency and risk measures from BMO martingales. Finance Stoch 12, 219–244 (2008). https://doi.org/10.1007/s00780-007-0057-1
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DOI: https://doi.org/10.1007/s00780-007-0057-1