Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/22266 
Authors: 
Year of Publication: 
2003
Series/Report no.: 
SFB 373 Discussion Paper No. 2003,53
Publisher: 
Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes, Berlin
Abstract: 
The paper provides an axiomatic characterization of dynamic risk measures for multi-period financial positions. For the special case of a terminal cash flow, we require that risk depends on its conditional distribution only. We prove a representation theorem for dynamic risk measures and investigate their relation to static risk measures. Two notions of dynamic consistency are proposed. A key insight of the paper is that dynamic consistency and the notion of 'measure convex sets of probability measures' are intimately related. Measure convexity can be interpreted using the concept of compound lotteries. We characterize the class of static risk measures that represent consistent dynamic risk measures. It turns out that these are closely connected to shortfall risk. Under weak additional assumptions, static convex risk measures coincide with shortfall risk, if compound lotteries of acceptable respectively rejected positions are again acceptable respectively rejected. This result implies a characterization of dynamically consistent convex risk measures.
Subjects: 
Dynamic risk measure
capital requirement
measure of risk
dynamic consistency
measure convexity
shortfall risk
JEL: 
G11
G28
G18
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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