Coherent risk measures and good-deal bounds

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Coherent risk measures and good-deal bounds

Author Info

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)

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.

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Article provided by Springer in its journal Finance and Stochastics.

Volume (Year): 5 (2001)
Issue (Month): 2 ()
Pages: 181-200
Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Handle: RePEc:spr:finsto:v:5:y:2001:i:2:p:181-200

Note: received: March 1999; final version received: March 2000
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Find related papers by JEL classification:
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets

Cited by:
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Takuji Arai, 2008. "Good deal bounds induced by shortfall risk," Quantitative Finance Papers 0802.4141, arXiv.org. [Downloadable!]
Ignacio Cascos & Ilya Molchanov, 2006. "Multivariate risks and depth-trimmed regions," Quantitative Finance Papers math/0606520, arXiv.org, revised Nov 2006. [Downloadable!]
Traian A. Pirvu & Gordan Zitkovic, 2007. "Maximizing the Growth Rate under Risk Constraints," Quantitative Finance Papers 0706.0480, arXiv.org. [Downloadable!]
Kerkhof, J. & Melenberg, B. & Schumacher, H., 2002. "Model risk and regulatory capital," Discussion Paper 27, Tilburg University, Center for Economic Research. [Downloadable!]
Oleg Bondarenko & Iñaki Longarela, 2009. "A general framework for the derivation of asset price bounds: an application to stochastic volatility option models," Review of Derivatives Research, Springer, vol. 12(2), pages 81-107, July. [Downloadable!] (restricted)
Ignacio Cascos & Ilya Molchanov, 2007. "Multivariate risks and depth-trimmed regions," Finance and Stochastics, Springer, vol. 11(3), pages 373-397, July. [Downloadable!] (restricted)

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