Let X_1,X_2,... be a sequence of [0,1]-valued i.i.d. random variables, let
c\geq 0 be a sampling cost for each observation and let Y_i=X_i-ic, i=1,2,....
For n=1,2,..., let M(Y_1,...,Y_n)=E(max_{1\leq i\leq n}Y_i) and
V(Y_1,...,Y_n)=sup_{\tau \in C^n}E(Y_{\tau}), where C^n denotes the set of all
stopping rules for Y_1,...,Y_n. Sharp upper bounds for the difference
M(Y_1,...,Y_n)-V(Y_1,...,Y_n) are given under various restrictions on c and n.Comment: Published at http://dx.doi.org/10.1214/009117904000000496 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
