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Optimal reinsurance revisited - a geometric approach. (English) Zbl 1230.91070
Summary: We reexamine the two optimal reinsurance problems studied in [J. Cai et al., Insur. Math. Econ. 43, No. 1, 185–196 (2008; Zbl 1140.91417)], in which the objectives are to find the optimal reinsurance contracts that minimize the value-at-risk (VaR) and the conditional tail expectation (CTE) of the total risk exposure under the expectation premium principle. We provide a simpler and more transparent approach to solve these problems by using intuitive geometric arguments. The usefulness of this approach is further demonstrated by solving the VaR-minimization problem when the expectation premium principle is replaced by Wang’s premium principle.

MSC:
91B30 Risk theory, insurance (MSC2010)
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