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We study the risk assessment of uncertain cash flows in terms of dynamicconvex risk measures for processes as introduced in Cheridito, Delbaen, andKupper (2006). These risk measures take into account not only the amounts butalso the timing of a cash flow. We discuss their robust representation in termsof suitably penalized probability measures on the optional sigma-field. Thisyields an explicit analysis both of model and discounting ambiguity. We focuson supermartingale criteria for different notions of time consistency. Inparticular we show how bubbles may appear in the dynamic penalization, and howthey cause a breakdown of asymptotic safety of the risk assessment procedure.

Risk assessment for uncertain cash flows: Model ambiguity, discounting ambiguity, and the role of bubbles