Limiting properties of the discounted house-selling problem

A class of sequential decision problems is considered in which selling opportunities are randomly distributed. According to problem formulation, a given number of property units must be sold unit-by-unit before a specified time. For each buying offer received, the owner must determine whether to accept the offer or reject it in hopes of receiving more attractive future offers. Offering prices are unknown until they are received, and once an offer is rejected there will be no more opportunities for its acceptance. At the time of the selling deadline, the owner will be charged a known fixed price for each unit that remains unsold. An optimal decision rule for the problem is developed for maximizing the present value of selected offers, and its asymptotic behavioral properties are investigated.