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Finance and Stochastics

, Volume 5, Issue 2, pp 181–200 | Cite as

Coherent risk measures and good-deal bounds

  • Stefan Jaschke
  • Uwe Küchler
Original Paper

Abstract.

The relation between coherent risk measures, valuation bounds, and certain classes of portfolio optimization problems is established. One of the key results is that coherent risk measures are essentially equivalent to generalized arbitrage bounds, named “good deal bounds” by Cerny and Hodges (1999). The results are economically general in the sense that they work for any cash stream spaces, be it in dynamic trading settings, one-step models, or deterministic cash streams. They are also mathematically general as they work in (possibly infinite-dimensional) linear spaces.

The valuation theory presented seems to fill a gap between arbitrage valuation on the one hand and utility maximization (or equilibrium theory) on the other hand. “Coherent” valuation bounds strike a balance in that the bounds can be sharp enough to be useful in the practice of pricing and still be generic, i.e., somewhat independent of personal preferences, in the way many coherent risk measures are somewhat generic.

Key words: Coherent risk measures, valuation bounds, portfolio optimization, robust hedging, convex duality 
JEL Classification: C61, G13, D52 
Mathematics Subject Classification (1991): 90A99, 90C25, 46E99 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Stefan Jaschke
    • 1
  • Uwe Küchler
    • 2
  1. 1.Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstrasse 39, 10117 Berlin, Germany (e-mail: stefan@jaschke.net) DE
  2. 2.Humboldt-Universität zu Berlin, Institut für Mathematik, Rudower Chaussee 25, 12489 Berlin, Germany (e-mail: kuechler@mathematik.hu-berlin.de) DE

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