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Dynamic risk measures: Time consistency and risk measures from BMO martingales

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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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  1. Centre de Mathématiques Appliquées (CMAP, UMR CNRS 7641), Ecole Polytechnique, 91128, Palaiseau cedex, France

    Jocelyne Bion-Nadal

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  1. Jocelyne Bion-Nadal
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Correspondence to Jocelyne Bion-Nadal.

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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

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