Distribution-Invariant Dynamic Risk Measures
AbstractThe 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. --
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Bibliographic InfoPaper provided by Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes in its series SFB 373 Discussion Papers with number 2003,53.
Date of creation: 2003
Date of revision:
Dynamic risk measure; capital requirement; measure of risk; dynamic consistency; measure convexity; shortfall risk;
Find related papers by JEL classification:
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
- G28 - Financial Economics - - Financial Institutions and Services - - - Government Policy and Regulation
- G18 - Financial Economics - - General Financial Markets - - - Government Policy and Regulation
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