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An optimal k-stopping problem for the Poisson process. (English) Zbl 0642.60031
Mathematical statistics and probability theory, Proc. 6th Pannonian Symp., Bad Tatzmannsdorf/Austria 1986, Vol. B, 231-244 (1987).
[For the entire collection see Zbl 0625.00018.]
Assume that the owner of k, \(k>1\), commodities of the same kind wants to sell them. Sequentially he receives offers which he has to refuse or accept immediately on arrival. Offers arrive according to a Poisson process. These offers are i.i.d. random variables discounted by some deterministic function of time.
The author presents an optimal strategy for the seller and explicitly computes some examples. He maximizes the discounted expected gain of the seller.
Reviewer: Z.Rychlik

MSC:
60G40 Stopping times; optimal stopping problems; gambling theory
62L15 Optimal stopping in statistics