Hattendorff's theorem and Thiele's differential equation generalized

Hattendorff's classical result on zero means an uncorrelatedness of the losses created in disjoint time intervals by a life insurance policy is an immediate consequence of the very definition of the concept of loss. Thus, the result is formulated and proved here in a setting with quite general payments, discount function, and time intervals, all stochastic. A general representation is given for the variances of the losses. They are easy to compute when sufficient structure is added to the model. The traditional continuous time Markov chain model is given special consideration. A stochastic Thiele's differential equation is obtained in a fairly general counting process framework.