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We study the risk assessment of uncertain cash flows in terms of dynamic convex risk measures for processes as introduced in Cheridito, Delbaen, and Kupper (2006). These risk measures take into account not only the amounts but also the timing of a cash flow. We discuss their robust representation in terms of suitably penalized probability measures on the optional $\sigma$-field. This yields an explicit analysis both of model and discounting ambiguity. We focus on supermartingale criteria for time consistency. In particular we show how ``bubbles'' may appear in the dynamic penalization, and how they cause a breakdown of asymptotic safety of the risk assessment procedure.
Dynamic risk measures
(2010)
This paper gives an overview of the theory of dynamic convex risk measures for random variables in discrete time setting. We summarize robust representation results of conditional convex risk measures, and we characterize various time consistency properties of dynamic risk measures in terms of acceptance sets, penalty functions, and by supermartingale properties of risk processes and penalty functions.