Journal of Mathematical Sciences: Advances and ApplicationsAuthor's: Werner Hürlimann
Pages: [21] - [47]
Received Date: November 30, 2014
Submitted by:
Within the set of financial losses with equal means and variances, a sound coherent distortion risk measure should preserve some higher degree stop-loss order, e.g., the degree three convex order. Risk measures that satisfy this property are called tail-free risk measures. Restricting the set of terminal values of martingale financial losses to biatomic, Weibull and Pareto losses, we show that a specific distortion measure is a tail-free coherent measure and satisfies a meaningful extra condition used to measure the risk of such financial losses. This main result is applied to derive an optimal economic capital formula for lookback financial losses. It is used to compare the riskiness of two investment strategies.
coherent risk measure, distortion risk measure, tail-free risk measure, higher degree convex order, lookback risk, economic capital.
