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Optimal reinsurance and stop-loss order. (English) Zbl 0986.62085
Summary: During the last two decades, the interest of the actuarial literature in stochastic orderings has been growing to such a point that they become one of the most important tools to compare the riskiness of different random situations. Our purpose in this note is to derive new results about the optimal reinsurance coverages for the ceding company, when the optimality criterion consists in minimizing the retained risk with respect to the stop-loss order. We so slightly complete the study initiated by A.E. van Heerwaarden, R. Kaas and M.J. Goovaerts [ibid. 8, No. 1, 11–17 (1989; Zbl 0683.62060)].

MSC:
62P05 Applications of statistics to actuarial sciences and financial mathematics
60E15 Inequalities; stochastic orderings
91B30 Risk theory, insurance (MSC2010)
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