Extending pricing rules with general risk functions |
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Authors: | Alejandro Balbás Raquel Balbás José Garrido |
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Institution: | 1. University Carlos III of Madrid, Department of Business Economics, CL, Madrid 126, 28903 Getafe, Madrid, Spain;2. University Complutense of Madrid, Department of Actuarial and Financial Economics, Somosaguas Campus, 28223 Pozuelo de Alarcón, Madrid, Spain;3. Concordia University, Department of Mathematics and Statistics, 1455 Boulevard de Maisonneuve Ouest, Montreal, Quebec, Canada H3G1M8 |
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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 Conditional Value at Risk and some properties of the Standard Deviation. Applications dealing with the valuation of volatility linked derivatives are discussed. |
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Keywords: | Incomplete and imperfect market Risk measure and deviation measure Pricing rule Convex optimization Optimality conditions |
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