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

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

2010-02-19

arxiv.org/abs/1002.3627v1

Economy

Quantitative Finance

Risk Management

40 pages

Scientific paper

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 different notions of 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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