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The secretary problem: Optimal selection with interview cost. (English) Zbl 0787.62084
Summary: We consider a new version of the secretary problem with loss equal to rank plus interview cost. The optimal rule is derived and is illustrated for certain cost functions and a few chosen values of \(n\) \((n\) denotes the total number of candidates). The approximating differential equations are obtained. An explicit solution to the problem with zero interview cost is obtained. For certain cost functions, explicit solutions of the differential equations are derived.
62L15 Optimal stopping in statistics
60G40 Stopping times; optimal stopping problems; gambling theory