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

Please always quote using this URN:urn:nbn:de:0296-matheon-7141
  • 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.

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Metadaten
Author:Beatrice Acciaio, Hans Föllmer, Irina Penner
URN:urn:nbn:de:0296-matheon-7141
Referee:Dirk Becherer
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2010/09/23
Release Date:2010/09/23
Tag:
Institute:Humboldt-Universität zu Berlin
MSC-Classification:60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Gxx Stochastic processes / 60G35 Signal detection and filtering [See also 62M20, 93E10, 93E11, 94Axx]
91-XX GAME THEORY, ECONOMICS, SOCIAL AND BEHAVIORAL SCIENCES / 91Bxx Mathematical economics (For econometrics, see 62P20) / 91B16 Utility theory
91-XX GAME THEORY, ECONOMICS, SOCIAL AND BEHAVIORAL SCIENCES / 91Bxx Mathematical economics (For econometrics, see 62P20) / 91B30 Risk theory, insurance
Preprint Number:724
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