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On a subjective approach to risk measurement 

Author: Piotr Jaworski a
Affiliation:   a Institute of Mathematics, Warsaw University, 02-097 Warszawa, Poland
DOI: 10.1080/14697680600739120
Publication Frequency: 8 issues per year
Published in: journal Quantitative Finance, Volume 6, Issue 6 December 2006 , pages 495 - 511
Formats available: HTML (English) : PDF (English)
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Abstract

This study is based on the analogy between hedging a risky asset and keeping reserves to meet an unknown demand. The optimal hedging level, which depends on individual preferences, is regarded as a measure of risk. We determine the set of optimal levels and investigate the properties of the associated risk measures. This approach provides a new insight into Value at Risk (VaR). We consider it as a solution of a certain optimal inventory problem with linear cost and loss functions. We show that these functions determine the confidence level of VaR. In this way we obtain a simple model that helps us to choose a proper confidence level agr and explains why supervisory institutions (such as the Basle Committee) choose a higher agr than financial institutions themselves.
Keywords: Risk measures; Value at Risk; Inventory theory; Stochastic optimization; Convex analysis
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