Reference : Risk assessment for uncertain cash flows: model ambiguity, discounting ambiguity, and...
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Risk assessment for uncertain cash flows: model ambiguity, discounting ambiguity, and the role of bubbles
Föllmer, Hans [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Acciaio, Beatrice []
Penner, Irina []
Finance and Stochastics
Springer Science & Business Media B.V.
Yes (verified by ORBilu)
[en] Dynamic convex risk measures ; Cash flows ; Discounting ambiguity ; Model ambiguity ; Robust representation ; Time consistency ; Dynamic penalisatio ; Asymptotic safety ; Bubbles ; Cash subadditivity
[en] We study the risk assessment of uncertain cash flows in terms of dynamic convex risk measures for processes as introduced in Cheridito et al. (Electron. J. Probab. 11(3):57–106, 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 penalised probability measures on the optional σ-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 penalisation, and how they cause a breakdown of asymptotic safety of the risk assessment procedure.

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