Applied Probability Trust (24 March 2004) STOPPING THE MAXIMUM OF A CORRELATED RANDOM WALK, WITH COST FOR OBSERVATION
نویسندگان
چکیده
Let (Sn)n≥0 be a correlated random walk on the integers, let M0 ≥ S0 be an arbitrary integer, and let Mn = max{M0, S1, . . . , Sn}. An optimal stopping rule is derived for the sequence Mn − nc, where c > 0 is a fixed cost. The optimal rule is shown to be of threshold type: stop the first time that Mn−Sn ≥ ∆, where ∆ is a certain nonnegative integer. An explicit expression for this optimal threshold is given.
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