Risk, Entropy, and the Transformation of Distributions

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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.

Published In:

North American Actuarial Journal (1092-0277)
April 2003. Vol. 7, Iss. 2, pp. 128-44