Distribution-Invariant Dynamic Risk Measures

Stefan Weber

No 2003,53, SFB 373 Discussion Papers from Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes

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.

Keywords: Dynamic risk measure; capital requirement; measure of risk; dynamic consistency; measure convexity; shortfall risk (search for similar items in EconPapers)
JEL-codes: G11 G18 G28 (search for similar items in EconPapers)
Date: 2003
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:zbw:sfb373:200353

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