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Risk, Entropy, and the Transformation of Distributions

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  • Mark Reesor
  • Don McLeish

Abstract

The exponential family, relative entropy, and distortion are methods of transforming probability distributions. We establish a link between those methods, focusing on the relation between relative entropy and distortion. Relative entropy is commonly used to price risky financial assets in incomplete markets, while distortion is widely used to price insurance risks and in risk management. The link between relative entropy and distortion provides some intuition behind distorted risk measures such as value-at-risk. Furthermore, distorted risk measures that have desirable properties, such as coherence, are easily generated via relative entropy.

Suggested Citation

  • Mark Reesor & Don McLeish, 2002. "Risk, Entropy, and the Transformation of Distributions," Staff Working Papers 02-11, Bank of Canada.
    • Handle: RePEc:bca:bocawp:02-11
    DOI: 10.34989/swp-2002-11
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    References listed on IDEAS

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    1. Wang, Shaun & Dhaene, Jan, 1998. "Comonotonicity, correlation order and premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 22(3), pages 235-242, July.
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    4. Lynn Wirch, Julia & Hardy, Mary R., 1999. "A synthesis of risk measures for capital adequacy," Insurance: Mathematics and Economics, Elsevier, vol. 25(3), pages 337-347, December.
    5. Shaun, Wang, 1995. "Insurance pricing and increased limits ratemaking by proportional hazards transforms," Insurance: Mathematics and Economics, Elsevier, vol. 17(1), pages 43-54, August.
    6. Wang, Shaun S. & Young, Virginia R. & Panjer, Harry H., 1997. "Axiomatic characterization of insurance prices," Insurance: Mathematics and Economics, Elsevier, vol. 21(2), pages 173-183, November.
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    Cited by:

    1. Schinckus, Christophe, 2018. "The valuation of social impact bonds: An introductory perspective with the Peterborough SIB," Research in International Business and Finance, Elsevier, vol. 45(C), pages 1-6.

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    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty
    • G0 - Financial Economics - - General

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