Publication: Extending pricing rules with general risk functions
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2010-02
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Elsevier
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Abstract
The paper addresses pricing issues in imperfect and/or incomplete markets if the risk level of the hedging
strategy is measured by a general risk function. Convex Optimization Theory is used in order to extend
pricing rules for a wide family of risk functions, including Deviation Measures, Expectation Bounded Risk
Measures and Coherent Measures of Risk. Necessary and sufficient optimality conditions are provided in
a very general setting. For imperfect markets the extended pricing rules reduce the bid ask spread. The
findings are particularized so as to study with more detail some concrete examples, including the Condi
tional Value at Risk and some properties of the Standard Deviation. Applications dealing with the valu
ation of volatility linked derivatives are discussed.
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Keywords
Incomplete market, Risk measure, Pricing rule, Convex optimization
Bibliographic citation
European Journal of Operational Research, 2010 v. 201, nº 1, pp. 23-33