Bather considered a buyer's problem and reduced it to an optimal stopping problem. In this note it is shown that this optimal stopping problem can be related to the sequential testing of the sign of the drift parameter of a Wiener process problem considered by Chernoff. Hence the asymptotic expansions for the sequential testing problem can be used in the buyer's problem.
"A Note on the Buyer's Problem." Ann. Statist. 15 (3) 1329 - 1331, September, 1987. https://doi.org/10.1214/aos/1176350510