Abstract
We study the relation between the properties of the coherent risk measures and of the heavy-tailed distributions from radial subsets of random variables. As a result, a new risk measure is introduced for this type of random variable. Under the assumptions of the Lundberg and renewal risk models, the solvency capital in the class of distributions with dominatedly varying tails is calculated. Further, the existence and uniqueness of the solution in the optimisation problem, associated to the minimisation of the risk over a set of financial positions, is investigated. The optimisation results hold on the \(L^{1+\varepsilon }\)-spaces, for any \(\varepsilon \ge 0\), but the uniqueness collapses on \(L^{1}\), the canonical space for the law-invariant coherent risk measures.
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Konstantinides, D.G., Kountzakis, C.E. (2014). Coherent Risk Measures Under Dominated Variation. In: Silvestrov, D., Martin-Löf, A. (eds) Modern Problems in Insurance Mathematics. EAA Series. Springer, Cham. https://doi.org/10.1007/978-3-319-06653-0_8
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