Explicit results for a class of asset-selling problems

Israel David

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10 Scopus citations


We consider the following optimal selection problem: There are n identical assets which are to be sold, one at a time, to coming bidders. The bids are i.i.d. where there are only two possible bid-values, with known probabilities. The stream of bidders constitutes a general renewal process, and rewards are continuously discounted at a constant rate. The objective is to maximize the total expected discounted revenue from the sale of the n assets. The optimal policy here is stationary, where the decision in question is only whether to accept a low bid or not; the answer is affirmative depending on a critical number n * of remaining assets. In this paper we derive an explicit formula for n *, being a function of the Laplace transform of the renewal distribution evaluated at the discount rate, the probability for a low bid, and the ratio between the two bid-values. We also specify the pertinent value functions. Applications of the model are discussed in detail, and extensions are made to include holding costs and to allow for optimal pricing.

Original languageEnglish
Pages (from-to)576-584
Number of pages9
JournalEuropean Journal of Operational Research
Issue number3
StatePublished - 1 Nov 1998
Externally publishedYes


  • Asset selling
  • Dynamic programming
  • Pricing
  • Secretary problems


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