Estimation of an exponential quantile under pitman's measure of closeness

We consider the problem of estimating a quantile of an exponential distribution with unknown location and scale parameters under Pitman's measure of closeness (PMC). The loss function is required to satisfy some mild conditions but is otherwise arbitrary. An optimal estimator is obtained in the class of location-scale-equivariant estimators, and its admissibility in the sense of PMC is investigated.