Explicit results for a class of asset-selling problems

✍ Scribed by Israel David

• Book ID: 104339587
• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 610 KB
• Volume: 110
• Category: Article
• ISSN: 0377-2217
• DOI: 10.1016/s0377-2217(97)00298-1

✦ Synopsis

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.