On a Theorem of Wald and Wolfowitz on Randomization in Statistics.
Suppose that at any stage of a statistical experiment a control variable that affects the distribution of the observed data at this stage can be used. The distribution of depends on some unknown parameter , and we consider the problem of testing multiple hypotheses , , allowing the data to be controlled by , in the following sequential context. The experiment starts with assigning a value to the control variable and observing as a response. After some analysis, another value for...
Optimal arrangement of a stream of insurance premiums for a multiperiod insurance policy is considered. In order to satisfy solvency requirements we assume that a weak Axiom of Solvency is satisfied. Then two optimization problems are solved: finding a stream of net premiums that approximates optimally 1) future claims, or 2) "anticipating premiums". It is shown that the resulting optimal streams of premiums enable differentiating between policyholders much more quickly than one-period credibility...