Coherent risk measures and good-deal bounds

Stefan Jaschke () and Uwe Küchler ()
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Stefan Jaschke: Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstrasse 39, 10117 Berlin, Germany
Uwe Küchler: Humboldt-Universität zu Berlin, Institut für Mathematik, Rudower Chaussee 25, 12489 Berlin, Germany Manuscript

Finance and Stochastics, 2001, vol. 5, issue 2, pages 181-200

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.

Keywords: Coherent risk measures; valuation bounds; portfolio optimization; robust hedging; convex duality (search for similar items in EconPapers)
JEL-codes: C61 G13 D52 (search for similar items in EconPapers)
Date: 2001-04-10
Note: received: March 1999; final version received: March 2000
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