Risk comparisons of premium rules: optimality and a life insurance study
Consider a risk Y-1 (x) depending on an observable covariate x which is the outcome of a random variable A with a known distribution, and consider a premium p(x) of the form p(x) = EY1 (x) + etap(1) (x). The corresponding adjustment coefficient gamma is the solution of E exp{gamma[Y-1(A) - p(A)]} = 1, and we characterize the rule for the loading premium p(1)((.)) which maximizes gamma subject to t