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Optimal risk transfer under quantile-based risk measurers

Asimit, A.V., Badescu, A. & Verdonck, T. (2013). Optimal risk transfer under quantile-based risk measurers. Insurance: Mathematics and Economics, 53(1), pp. 252-265. doi: 10.1016/j.insmatheco.2013.05.005


The classical problem of identifying the optimal risk transfer from one insurance company to multiple reinsurance companies is examined under some quantile-based risk measure criteria. We develop a new methodology via a two-stage optimisation procedure which not only allows us to recover some existing results in the literature, but also makes possible the analysis of high-dimensional problems in which the insurance company diversifies its risk with multiple reinsurance counter-parties, where the insurer risk position and the premium charged by the reinsurers are functions of the underlying risk quantile. Closed-form solutions are elaborated for some particular settings, although numerical methods for the second part of our procedure represent viable alternatives for the ease of implementing it in more complex scenarios. Furthermore, we discuss some approaches to obtain more robust results.

Publication Type: Article
Additional Information: © 2015, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
Publisher Keywords: Expected shortfall; Distorted risk measure; Premium principle; Optimal reinsurance; Truncated tail value-at-risk; Value-at-risk
Subjects: H Social Sciences > HD Industries. Land use. Labor > HD61 Risk Management
Departments: Bayes Business School > Actuarial Science & Insurance
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