On multiple stopping rules

Abstract

A multiple (k-)stopping rule with respect to σ-algebras [formula omitted] is a sequence of k stopping times [formula omitted]. If [formula omitted] is [formula omitted]-measurable and integrable for all [formula omitted], the aim is to find [formula omitted] such that [formula omitted] 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 ease 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 detail, Finally a new rank selection problem is solved. © 1985 Taylor & Francis Group, LLC. All Rights Reserved.