We prove that classical estimators and pseudo-estimators used in the Buhlmann-Straub credibility theory model are optimal, in the sense of minimum variance, under zero excess assumptions on the involved random variables.
Devylder, F., & Goovaerts, M. (1992). Optimal Parameter-estimation Under Zero Excess Assumptions in the Buhlmann-straub Model. Insurance: Mathematics and Economics, 11(3), 167-171. https://doi.org/10.1016/0167-6687(92)90023-5 (Original work published 1992)