Inspired by the recent discussion about cash-additivite risk measures, we investigate under which conditions cash-subadditive convex dynamic risk measures are time-consistent. Proceeding as in Detlefsen and Scandolo (2005) and inspired by their result, we give a dual representation of dynamic cash-subadditive convex risk measures (that can also be seen as particular case of the dual quasiconvex representation). Furthermore, we will provide, in the cash-subadditive case, a sufficient condition for strong time-consistency in terms of a generalized cocycle condition. Finally, we exploit the relation between different notions of time-consistency.
Joint work with E. Mastrogiacomo.