Approximation to optimal stopping rules for gamma random variables with unknown location and scale parameters

Let X-1, X-2,...,X-n,... be independent, identically distributed gamma random variables with unknown location and scale parameters. If we define the reward sequence Y-n = max{X-1, X-2,..., X-n} - cn, for c > 0, the optimal stopping rule for Y-n depends on the unknown parameters. In this paper, we propose an adaptive stopping rule that does not depend on the parameters and show that the difference between the optimal expected reward and the expected reward using the proposed adaptive stopping rule vanishes as c goes to zero.