Distribution-Invariant Dynamic Risk Measures

Arbeitspapier

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.

Angaben zum Objekt

• Sprache: Englisch

Verweise und Beziehungen

• Erschienen in: Series: SFB 373 Discussion Paper ; No. 2003,53

Klassifikation und Themen

• Klassifikation: Wirtschaft ; Portfolio Choice; Investment Decisions ; Financial Institutions and Services: Government Policy and Regulation ; General Financial Markets: Government Policy and Regulation
• Thema: Dynamic risk measure ; capital requirement ; measure of risk ; dynamic consistency ; measure convexity ; shortfall risk ; Risiko ; Messung ; Portfolio-Management ; Dynamisches Modell ; Theorie

Beteiligte, Orts- und Zeitangaben

• Ereignis: Geistige Schöpfung
• (wer): Weber, Stefan
• Ereignis: Veröffentlichung
• (wer): Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes
• (wo): Berlin
• (wann): 2003

Weitere Informationen

• Handle: http://hdl.handle.net/10419/22266
• URN: urn:nbn:de:kobv:11-10050879
• Letzte Aktualisierung: 10.03.2025, 11:41 MEZ