TY - JOUR

T1 - Explicit results for a class of asset-selling problems

AU - David, Israel

PY - 1998/11/1

Y1 - 1998/11/1

N2 - 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.

AB - 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.

KW - Asset selling

KW - Dynamic programming

KW - Pricing

KW - Secretary problems

UR - http://www.scopus.com/inward/record.url?scp=0032210050&partnerID=8YFLogxK

U2 - 10.1016/s0377-2217(97)00298-1

DO - 10.1016/s0377-2217(97)00298-1

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AN - SCOPUS:0032210050

SN - 0377-2217

VL - 110

SP - 576

EP - 584

JO - European Journal of Operational Research

JF - European Journal of Operational Research

IS - 3

ER -