This paper presents a discrete-time sequential stochastic asset-selling problem with an infinite planning horizon, where the process of selling the asset may reach a deadline at any point in time with a probability. It is assumed that a quitting offer is available at every point in time and search skipping is permitted. Thus, decisions must be made as to whether or not to accept the quitting offer, to accept an appearing buyer’s offer, and to conduct a search for a buyer. The main purpose of this paper is to clarify the properties of the optimal decision rules in relation to the model’s parameters.
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