On multiple stopping bales

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Abstract
A multiple (k-)stopping rule with respect to σ-algebras is a sequenee of k stopping times . If measurable and integrable for all , the aim is to find such that is maximized. This yields a new class of stopping problems including the rank selection problems of Platen ([4]). Some general theorems on optimal k-stopping rules are proved and then applied to several examples. E.g. for the case of choosing k out of N independent sequentially appearing random values such that the expected sum is maximal the asymptotic behavior of the “pay-off” is studied in cletaiL Finallv a new rank selection problem is solved.

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