The full-information best-choice problem with uniform or gamma horizons

Abstract

A decision-maker has to choose one from among a Poisson stream of i.i.d. bids, with no recall. The stream stops at a random time with a uniform (in the first case) or Erlang (in the second case) distribution. We solve the problem explicitly for maximal expected gain for bids that may take on any finite number of values. A fast procedure to solve the problem for fixed horizon is presented as well.

Keywords:

• full-information secretary problems
• random horizon
• fixed horizon
• dynamic programming

AMS Subject Classifications:

• 90C39
• 60G40

Notes

No potential conflict of interest was reported by the authors.